Welcome to Lesson 1

In this first module of our course, we begin with a question that seems simple but unlocks the workings of our entire universe: What is energy?

In physics, energy is defined as the capacity to do work or produce heat. You can’t hold energy in your hand like a rock—but you see its effects everywhere. It’s what lets your heartbeat, your phone light up, a wind turbine spin, and the sunshine. Energy isn’t a “thing” itself, it’s a property of systems that enables change, motion, and transformation.

Energy comes in many forms, and one of its most fascinating features is that it can change from one type to another, but it’s never created or destroyed. This is the Law of Conservation of Energy, a cornerstone of science.

We’ll explore six key forms of energy that shape our daily lives:

• Mechanical energy -the sum of kinetic energy (motion) and potential energy stored due to position or condition, like a roller coaster at the top of a hill or a spinning bicycle wheel.
• Chemical energy, stored in the bonds of molecules, found in food, gasoline, and batteries, and released when those bonds break.
• Thermal (heat) energy, the total microscopic kinetic and potential energy of vibrating atoms and molecules—felt in a warm cup of tea or the friction of brakes on a bike.
• Electrical energy, carried by moving electrons through wires powers everything from LED lights to electric cars.
• Radiant (or electromagnetic) energy, which travels as waves, from visible light and radio signals to X-rays and infrared heat.
• Nuclear energy released when atomic nuclei split (fission) or fuse (fusion), powering stars like our Sun and nuclear reactors on Earth.

But understanding energy isn’t just about naming its forms it’s about seeing how it flows and transforms. For example:

• Your body converts chemical energy from food into mechanical energy (to walk or type), thermal energy (to stay warm), and even electrical signals in your nerves.
• A car engine turns the chemical energy in gasoline into thermal energy through combustion, then into mechanical energy to move the wheels—though much is lost as waste heat.
• Solar panels capture radiant energy from the Sun and convert it directly into electrical energy to power homes.

Finally, we’ll examine where our energy comes from. Most of the world still relies on nonrenewable sources like coal, oil, and natural gas, fossil fuels formed over millions of years. But cleaner, sustainable renewable sources—such as sunlight, wind, water, and geothermal heat—are rapidly growing and offer a path toward a healthier planet.

By the end of this module, you’ll not only understand what energy is, you’ll be able to trace its journey through your morning routine, your city’s power grid, and even the core of the Sun. You’ll see energy not as an abstract concept, but as the invisible thread connecting physics, technology, biology, and environmental stewardship.

So let’s dive in—and start seeing the world through the lens of energy!

Lesson 1: Learning Objectives

Upon completing this lesson, you should be able to:

• Define energy using the physics definition: the capacity to do work or produce heat
• State the Law of Conservation of Energy and explain its significance in scientific analysis
• Identify the six key forms of energy: mechanical, chemical, thermal, electrical, radiant, and nuclear
• Describe the difference between kinetic energy (energy of motion) and potential energy (stored energy)
• Distinguish between renewable and nonrenewable energy sources with at least two examples of each

Energy is the ability to do work or cause change. It’s what makes things happen—whether it’s a car moving, a phone lighting up, your heart beating, or the sun warming your skin.

Importantly, energy cannot be created or destroyed—only transformed from one form to another (this is the Law of Conservation of Energy). That means the energy in your morning coffee, your electric scooter, or even a lightning bolt all started somewhere else and changed forms along the way.

Scientists recognize many types of energy, but they all fall into a few fundamental categories. The U.S. Energy Information Administration (EIA) identifies six primary forms of energy that we use every day:

1. Mechanical Energy
2. Chemical Energy
3. Thermal (Heat) Energy
4. Electrical Energy
5. Radiant (Light) Energy
6. Nuclear Energy

Additionally, each energy source can be categorized as Kinetic Energy or Potential Energy. Kinetic Energy is the energy of motion. Potential Energy is stored energy, to be used later. We will discuss each of these forms of energy in the next sections.

Understanding Mechanical Energy: The Energy of Motion and Position

Energy is the ability to do work—whether that means moving an object, heating a room, or powering a phone. In our everyday lives, we constantly use energy in many forms: electrical, chemical, thermal, nuclear, radiant, and mechanical. Over the next few pages, we are going to investigate these different energy forms. Among these, mechanical energy is especially intuitive because it involves things we can see and feel—like cars moving, balls flying, or roller coasters zooming down hills.

Mechanical energy comes in two main types: kinetic energy (energy of motion) and potential energy (stored energy due to position or condition). Together, they help us understand how objects move and interact in the physical world.

Kinetic Energy: Energy in Motion

Kinetic energy is the energy an object has because it’s moving. The faster something moves—or the more massive it is—the more kinetic energy it carries.

Real-World Examples:

• A baseball pitcher throwing a fastball: The ball gains kinetic energy as it leaves the pitcher’s hand. That energy is what allows it to travel toward home plate at high speed.
• A freight train hauling cargo across the country: Even though it may seem slow, its huge mass gives it enormous kinetic energy—so much that it takes miles to stop safely!
• Wind turbines spinning in a field: The moving air (wind) has kinetic energy, which turns the turbine blades and generates electricity.
• You riding a bicycle downhill: As you pick up speed, your kinetic energy increases—you can feel it in the rush of wind and the momentum carrying you forward.

In the United States, about one-third of all energy consumption goes toward transportation—cars, trucks, planes, and ships—all of which rely on converting other forms of energy (like chemical energy in gasoline) into mechanical kinetic energy to move people and goods.

Potential Energy: Stored Energy Ready to Be Used

Potential energy is stored energy based on an object’s position, shape, or state. In mechanics, we often talk about gravitational potential energy (due to height) and elastic potential energy (due to stretching or compressing).

Gravitational Potential Energy Examples:

• A book on a high shelf: It doesn’t seem to be doing anything—but if it falls, gravity pulls it down, turning that stored energy into motion. The higher the shelf, the more potential energy the book has.
• Hydropower dams: Water held behind a dam has gravitational potential energy. When released, it flows downward, spinning turbines to generate electricity—converting potential energy into kinetic, then into electrical energy.
• A roller coaster at the top of a hill: At the peak, it’s momentarily still but packed with potential energy. As it plunges down, that energy transforms into thrilling speed (kinetic energy)

Elastic Potential Energy Examples:

• A drawn bow in archery: Pulling back the string stores energy in the bent limbs of the bow. When released, that energy propels the arrow forward.
• A compressed spring in a toy car: Wind it up, and you store elastic potential energy. Let go, and the spring uncoils, making the car zoom across the floor.
• Trampolines: When you land on one, the mat stretches downward, storing energy. That energy is then returned to you as you bounce back up!

The Earth-Book System: Why Context Matters

It’s important to remember that potential energy isn’t just “in” the object—it belongs to the system. Take the book on the shelf again: by itself, the book doesn’t “have” gravitational potential energy. It’s the combination of the book and the Earth’s gravitational field that creates this stored energy. If there were no gravity (like in deep space), the book wouldn’t gain speed when “dropped”—because there’d be nothing pulling it down.

So, when the book falls:

• The Earth-book system loses gravitational potential energy.
• That energy is converted into kinetic energy as the book accelerates downward.
• Just before it hits the floor, almost all the original potential energy has become kinetic energy.

This idea—that energy can change forms but isn’t created or destroyed—is part of the Law of Conservation of Energy, a fundamental principle in physics.

Bringing It All Together: Mechanical Energy in Action

Many real-world systems rely on the continuous conversion between potential and kinetic energy:

• Pendulum clocks: At the highest point of its swing, the pendulum has maximum potential energy and zero kinetic energy. At the bottom of the swing, it’s moving fastest—maximum kinetic energy, minimum potential energy. This back-and-forth exchange keeps the clock ticking.
• Skateboarders in a half-pipe: They start by dropping from the top (high potential energy), speed up at the bottom (high kinetic energy), then rise up the other side, slowing down as kinetic energy turns back into potential energy.
• Bungee jumping: The jumper starts with gravitational potential energy at the platform. As they fall, it becomes kinetic energy—until the bungee cord stretches, converting that kinetic energy into elastic potential energy, which then pulls them back up.

By understanding mechanical energy—how it’s stored, how it moves, and how it transforms—we gain insight into everything from simple toys to complex engineering systems. And the best part? You’re already using these principles every time you throw a ball, ride a bike, or even walk downstairs!

Chemical Energy: The Hidden Power in Molecules

Chemical energy is a form of potential energy stored in the bonds that hold atoms together inside molecules. Think of it like a coiled spring at the atomic level: even though nothing appears to be happening, a huge amount of energy is “locked away” until a chemical reaction unlocks it.

This energy exists because of the electromagnetic forces between electrons and nuclei in atoms. When atoms bond to form molecules (like glucose, gasoline, or methane), they settle into a stable arrangement that has a specific amount of stored energy. If those bonds are broken or rearranged during a chemical reaction—like burning, digesting, or discharging a battery—that stored energy can be released, often as heat, light, or mechanical work.

How Chemical Energy Becomes Useful Energy

Chemical energy rarely stays as chemical energy for long—it usually transforms into other forms we can use:

• Thermal energy (heat) – e.g., from burning wood
• Electrical energy – e.g., from a battery powering your phone
• Mechanical energy – e.g., your muscles contracting to lift a backpack
• Light energy – e.g., a glow stick or firefly

This transformation is what makes chemical energy so essential in both nature and technology.

Everyday Examples of Chemical Energy

1. Batteries (Portable Power)
   A AA battery doesn’t look like it’s doing much—but inside, a chemical reaction between zinc and manganese dioxide releases electrons. These electrons flow through a circuit, creating electrical energy that powers your remote, flashlight, or wireless mouse. Rechargeable batteries (like in phones or electric cars) reverse this process when plugged in, storing electrical energy back as chemical energy.

2. Food = Fuel for Your Body
   The glucose (a simple sugar) in your bloodstream is your body’s primary energy source. When you eat a banana or a slice of bread, your digestive system breaks it down into glucose. Inside your cells, glucose reacts with oxygen in a process called cellular respiration:

   ${\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}{\text{ + 6O}}_{\text{2}}{\text{→ 6CO}}_{\text{2}}{\text{ + 6H}}_{\text{2}}\text{O + Energy}$

   This reaction releases chemical energy, which your muscles convert into mechanical energy (to walk, jump, or type) and thermal energy (to keep you warm). Without this stored chemical energy, you couldn’t move or even breathe!

3. Burning Wood or Gasoline (Combustion)
   When you light a campfire, the cellulose and other compounds in wood react with oxygen. The chemical bonds break and reform into new molecules (like CO₂ and H₂O), releasing heat and light. The same thing happens in your car engine: gasoline combusts, producing hot, expanding gases that push pistons—converting chemical energy → thermal energy → mechanical energy to turn the wheels.
4. Fossil Fuels: America’s Primary Energy Source
   As of 2020, about 80% of U.S. energy came from fossil fuels—coal, oil, and natural gas. These fuels formed over millions of years from buried plants and microorganisms. Their molecules (like octane in gasoline or methane in natural gas) are packed with chemical energy.
   • In a power plant, coal is burned to heat water into steam, which spins turbines (chemical → thermal → mechanical → electrical).
   • In a gas stove, natural gas (mostly methane) burns to produce a flame for cooking (chemical → thermal + light).
   • In a jet engine, kerosene-based fuel combusts to create thrust (chemical → thermal → kinetic/mechanical).
5. Photosynthesis: Nature’s Energy Storage
   Plants do the opposite of combustion! They absorb sunlight and use it to build glucose from carbon dioxide and water. In this process, radiant (solar) energy is converted into chemical energy and stored in sugar molecules. This stored energy then moves through the food chain—when you eat a salad, you’re literally consuming sunlight that was captured and stored by plants!
6. Hand Warmers and Cold Packs
   • Disposable hand warmers contain iron powder that slowly oxidizes (rusts) when exposed to air a chemical reaction that releases heat.
   • Instant cold packs mix ammonium nitrate and water in a sealed bag. The dissolving process absorbs heat from the surroundings, making the pack feel cold. Both rely on changes in chemical potential energy!

Why Is Chemical Energy Considered “Potential”?

Just like a book on a shelf has gravitational potential energy because of its position, a molecule has chemical potential energy because of how its atoms are arranged. Until a reaction occurs, that energy stays hidden. But once the right conditions are met (like adding a spark, mixing chemicals, or activating an enzyme in your body), the energy is released—and often does useful work.

Importantly, the total energy is conserved. The “lost” chemical energy doesn’t vanish, it becomes heat, motion, light, or other forms. That’s why your laptop gets warm when charging (some energy becomes heat) or why you sweat during exercise (your body releases excess thermal energy from breaking down food).

Connecting Back to Mechanical Energy

One of the most important conversions in daily life is:

Chemical energy → Mechanical energy

• Your muscles convert glucose into motion.
• A car engine converts gasoline into wheel rotation.
• A rocket converts liquid hydrogen and oxygen into upward thrust.

In each case, stored molecular energy becomes macroscopic movement—linking the invisible world of atoms to the visible world of motion we experience every day.

Final Thought

From the food on your plate to the gas in your car, chemical energy is the silent powerhouse behind modern life. Understanding it helps us appreciate not just how things work—but also why energy choices (like switching from fossil fuels to biofuels or batteries) matter for our health, economy, and planet.

And remember: every time you take a step, send a text, or boil water for pasta—you’re tapping into the incredible power stored in chemical bonds!

Thermal (Heat) Energy: The Energy of Jiggling Molecule

Thermal energy—often called heat energy is the total internal energy contained within a substance due to the random motion and interactions of its atoms and molecules. It includes both:

• Microscopic kinetic energy: the energy of molecules moving, rotating, and vibrating.
• Microscopic potential energy: the energy stored in the forces between molecules (like tiny springs pulling or pushing on each other).

Unlike temperature, which tells us how hot or cold something feels, thermal energy depends on three things:

1. Temperature (how fast the molecules are jiggling),
2. Mass (how much stuff is there), and
3. Material (how tightly the molecules are bound, which affects how much energy they can store).

What Does “Hot” Really Mean?

When you say your coffee is “hot,” you’re really saying its molecules are moving and vibrating rapidly. In solids (like a metal spoon), atoms vibrate in place. In liquids (like soup), molecules slide past each other but still jiggle. In gases (like steam), molecules zip around freely at high speed.

The higher the temperature, the more intense this motion becomes—and the more microscopic kinetic energy the system has. At the same time, as molecules move farther apart (like when ice melts into water), their potential energy increases because they’re overcoming attractive forces—just like lifting a book off a shelf increases gravitational potential energy.

Thermal energy is a mix of tiny-scale kinetic and potential energy, all happening trillions of times per second!

Real-World Examples of Thermal Energy

1. A Hot Cup of Coffee
   Your morning coffee feels warm because its fast-moving water molecules collide with your skin, transferring energy. That warmth is thermal energy flowing from the coffee (high temperature) to your hand (lower temperature), a process called heat transfer.
2. Boiling Water on a Stove
   As you heat water, its molecules gain kinetic energy and move faster. At 100°C (212°F) at sea level, they have enough energy to break free from liquid bonds and become steam (gas). The bubbling you see is thermal energy causing a phase change—from liquid to gas.
3. Car Engines and Power Plants
   Most cars burn gasoline (chemical energy), which releases thermal energy through combustion. This heat causes gases to expand rapidly, pushing pistons → creating mechanical energy to turn the wheels.
   Similarly, coal or natural gas power plants burn fuel to heat water into steam, which spins turbines to generate electricity. In both cases:      Chemical → Thermal → Mechanical → Electrical
4. Your Body Produces Thermal Energy
   When you exercise, your muscles convert chemical energy (from food) into mechanical work, but not all of it! About 60–70% is “lost” as thermal energy, which is why you sweat. Your body uses this heat to maintain a stable internal temperature (~37°C or 98.6°F).

Why Thermal Energy Matters

• Energy conversions: Most human-made energy systems (cars, power plants, rockets) rely on converting other forms of energy into thermal energy first, then into useful work.
• Efficiency limits: Not all thermal energy can be turned into work, some always “escapes” as waste heat (this is governed by the Second Law of Thermodynamics). We will discuss this more in Lesson 2!
• Climate and environment: Burning fossil fuels releases huge amounts of thermal energy into the atmosphere, contributing to global warming. Understanding thermal energy helps us design better insulation, engines, and renewable technologies.

Final Thought

Thermal energy is everywhere—in your breath on a cold day, in the warmth of sunlight, in the hum of your laptop. It’s the invisible dance of trillions of molecules, constantly moving, colliding, and storing energy. And while we can’t see it directly, we feel it, use it, and depend on it every single day.

So next time you sip hot chocolate or feel the sun on your skin, remember you’re experiencing the collective motion of countless tiny particles—doing their energetic, chaotic, essential dance!

Electrical Energy – The Power of Moving Electrons

What Is Electrical Energy?

Electrical energy is the energy carried by the flow of electric charge, usually in the form of moving electrons through a conductor (like a copper wire). It’s not electricity itself that is energy, but rather, the movement of charged particles transfers energy from one place to another.

Think of it like water flowing through a pipe:

• The water is like the electrons.
• The flow (current) carries energy.
• The pump or height difference that pushes the water is like the voltage (electrical “pressure”).

This energy can be easily converted into other useful forms: heat, light, sound, or motion making electricity one of the most versatile and controllable forms of energy we use.

The Atomic Basis of Electricity

All matter is made of atoms, and atoms contain three key subatomic particles:
•Protons (positive charge) — in the nucleus (center)
•Neutrons (no charge) — also in the nucleus
•Electrons (negative charge) — orbit the nucleus in "shells"

In most materials, electrons are tightly bound to their atoms. But in conductors—especially metals like copper, aluminum, or silver—some electrons in the outer shells are loosely held. These are called free electrons.

When a voltage (electrical potential difference) is applied—say, by connecting a battery to a wire—it creates an electric field that pushes these free electrons to drift in one direction. This organized flow of electrons is called an electric current, and it carries electrical energy through the circuit.
 

How Electrical Energy Powers Our World: Real-World Conversions

One of the greatest strengths of electrical energy is how easily it transforms into other forms. Here’s how it works in everyday devices:

1. → Thermal Energy (Heat)
   • Toaster: Electric current flows through a thin wire (heating element) with high resistance. Electrons collide with atoms, making them vibrate faster → heat!
   • Electric stove, space heater, hair dryer: All use the same principle—resistive heating—to turn electricity into warmth.
2. → Light Energy
   • Incandescent bulb: Electricity heats a tungsten filament until it glows (also produces a lot of waste heat).
   • LED bulb: Electrons move through a semiconductor material, releasing energy directly as light—much more efficient!
   • Phone screen, traffic lights, holiday lights: All rely on controlled electrical-to-light conversion.
3. → Sound Energy
   • Stereo speakers: An electric signal causes a coil of wire to move back and forth inside a magnet. This vibrates a cone, creating sound waves.
   • Doorbells, alarms, headphones: All convert electrical signals into audible vibrations.
4. → Mechanical Energy (Motion)
   • Electric fan, blender, washing machine: Contain an electric motor. Inside, electricity creates magnetic fields that push against each other, causing a shaft to spin → mechanical energy.
   • Electric cars: Use powerful motors to turn electrical energy from batteries into wheel rotation—quiet, efficient, and zero emissions at the tailpipe!
5. → Chemical Energy (Storage)
   • Charging your phone: Electrical energy from the wall outlet drives a chemical reaction inside the lithium-ion battery, storing energy as chemical potential energy for later use.
   • Electrolysis: Electricity can split water (H₂O) into hydrogen and oxygen—storing energy in chemical bonds for future fuel.

Why Is Electrical Energy So Useful?

1. Easy to transport: Wires can carry it miles with minimal loss.
2. Instant control: Flip a switch: on or off in milliseconds.
3. Highly convertible: Turns efficiently into light, heat, motion, etc.
4. Clean at point of use: No smoke, noise, or fumes (even if the power plant isn’t clean).

That’s why everything from MRI machines to video game consoles relies on it!

Final Thought: You’re Part of the Circuit!

Your nervous system uses bioelectricity, tiny electrical signals created by the movement of ions (charged atoms) across nerve cells, to send messages from your brain to your toes. In a very real sense, you run on electrical energy too!

Next time you turn on a lamp, charge your phone, or ride an elevator, remember you’re harnessing the power of trillions of electrons on the move all working together to make modern life possible.

What Is Radiation?

Radiation simply means energy that travels through space or matter in the form of waves or particles. Despite the word sometimes sounding alarming, most radiation is completely harmless—and essential to life!

There are two main types of radiation we encounter:

1. Electromagnetic radiation (energy waves like light, radio, X-rays)
2. Nuclear (or particle) radiation (tiny particles emitted from unstable atoms)

In this module, we’ll focus mostly on electromagnetic radiation—the kind that powers everything from sunlight to Wi-Fi—and briefly touch on everyday sources of low-level nuclear radiation.

⚡ Electromagnetic Radiation: Energy on the Move

Electromagnetic (EM) radiation is energy that travels as oscillating electric and magnetic fields moving together through space at the speed of light (about 300,000 km/s!). It doesn’t need air or water to travel—which is why sunlight reaches us across the vacuum of space.

This energy comes in tiny “packets” called photons. Photons have no mass, but they carry energy—and the more energy a photon has, the shorter its wavelength.

The Electromagnetic Spectrum: One Family, Many Forms

All electromagnetic radiation—from radio waves to gamma rays—is fundamentally the same phenomenon, just with different wavelengths and energies. Scientists organize these into the electromagnetic spectrum:

Text description of the figure 1.1.

The image illustrates the electromagnetic spectrum, comparing different types of radiation from radio waves to gamma rays. It is organized into several sections, each providing different details about the characteristics of these waves. At the top, a wavy red line represents the increasing frequency from left (radio waves) to right (gamma rays). Immediately below, a row of rectangles indicates whether each radiation type penetrates Earth's atmosphere, with "Y" for yes and "N" for no.

The wave types are listed with their corresponding wavelengths in meters: Radio (10³), Microwave (10⁻²), Infrared (10⁻⁵), Visible (0.5×10⁻⁶), Ultraviolet (10⁻⁸), X-ray (10⁻¹⁰), Gamma ray (10⁻¹²). Each type is accompanied by an image for approximate scale: Buildings for radio, humans for microwave, butterflies for infrared, needle points for visible, protozoans for ultraviolet, molecules for X-ray, atoms for gamma ray, and atomic nuclei for the smallest scales.

Below, the frequency range in Hertz (Hz) is shown, mapping the spectrum from 10⁴ for radio waves to 10²⁰ for gamma rays. A colored horizontal bar displays the visible spectrum from red at the left to violet at the right.

The lowest section describes the temperature of objects emitting the most intense wavelength, depicted with a gradient bar ranging from 1 Kelvin (-272°C) to 10,000,000 Kelvin (~10,000,000°C).

Credit: EM Spectrum Properties edit.svg. (2025, December 21). Wikimedia Commons. Retrieved April 2, 2026.

Real-World Examples of Electromagnetic Radiation

• Sunlight: A mix of visible light, UV, and infrared—powers photosynthesis, warms Earth, and gives you a tan (or sunburn!).
• Wi-Fi & Bluetooth: Use microwaves to send data between your phone and router.
• Remote controls: Send infrared signals to your TV.
• Night-vision goggles: Detect infrared radiation (heat) emitted by people and animals.
• Medical X-rays: Pass through soft tissue but are absorbed by bones—creating diagnostic images.
• Solar panels: Capture photons from sunlight and convert them directly into electricity.

Please watch the following 5:04 video about the electromagnetic spectrum:

Tour of the Electro Magnetic Spectrum (5:03)

What Is Nuclear Energy?

Nuclear energy is the enormous amount of energy stored in the nucleus (core) of an atom. Unlike chemical energy—which involves electrons orbiting the nucleus—nuclear energy comes from forces inside the nucleus itself. When the structure of a nucleus changes, a tiny bit of its mass can be converted directly into vast amounts of energy, as described by Einstein’s famous equation:

Because the speed of light (c) is so huge (about 300,000,000 meters per second), c² is unimaginably large—meaning even a tiny amount of mass converts into a tremendous amount of energy.

There are two main ways to release nuclear energy: fission and fusion.

 Two Paths to Nuclear Energy: Fission vs. Fusion

 E = mc² in Action: Why So Much Energy?

Let’s put Einstein’s equation into perspective:

• If you could convert 1 gram of matter (about the mass of a paperclip) completely into energy, it would release:
  • 90 trillion joules—enough to power the average U.S. home for over 2,000 years!

In reality, nuclear reactions convert only about 0.1% to 0.7% of mass into energy—but that’s still millions of times more than burning the same mass of coal or oil.

 Comparison:

• Burning 1 kg of coal → ~30 million joules
• Fission of 1 kg of uranium → ~80 billion joules
• Fusion of 1 kg of hydrogen → ~300 billion joules

That’s the power of the nucleus!

Natural & Everyday Nuclear Energy

Nuclear processes aren’t just in reactors or stars—they’re part of our planet too:

• Earth’s interior heat: Partly comes from natural radioactive decay of uranium, thorium, and potassium in rocks—this drives plate tectonics and volcanoes.
• Geothermal energy: Harnesses this internal heat for clean electricity and heating.
• Carbon-14 dating: Uses natural radioactive decay to determine the age of ancient artifacts.

Final Thought: A Tiny Nucleus, Infinite Potential

Nuclear energy reminds us that the smallest things can have the biggest impact. From the sunlight that sustains life to the reactors that power cities, the energy locked inside atomic nuclei shapes our world.

While fission gives us clean electricity today, fusion offers hope for a nearly limitless, safe, and clean energy future. Understanding both helps us make informed choices about energy, climate, and innovation.

Below is a comprehensive visual representation of the six fundamental forms of energy we have explored in the previous sections. This infographic organizes energy into its primary categories—Mechanical, Thermal, Electrical, Electromagnetic, Chemical, and Nuclear each illustrated with examples that demonstrate how energy forms appear in our daily lives and in nature. Note that in this particular visualization, Electromagnetic energy is presented as a single category that encompasses both visible light (radiant energy) and radio waves, highlighting how these phenomena are fundamentally the same type of energy differing only in wavelength and frequency.

Text description of the Types of Energy image.

The image is an educational infographic titled "Types of Energy." It features a central blue circle labeled "Forms of Energy" connected by arrows to smaller blue circles, each labeled with different forms of energy: Mechanical, Thermal, Electrical, Electromagnetic, Chemical, and Nuclear. Each form of energy is illustrated with an icon. Mechanical energy is shown with a hammer and nail, and a moving car. Thermal energy is depicted with melting ice and heating food in an oven. Electrical energy is exemplified by lightning and power lines. Electromagnetic energy is represented by visible light and radio waves. Chemical energy is illustrated with a battery and food people eat. Nuclear energy is shown with nuclear fusion and fission illustrations.

Credit: © VectorMine / Adobe Stock.”Accessed May. 1, 2026. 

What Is Energy Conversion?

Energy conversion (or energy transformation) is the process of changing energy from one form into another. This happens constantly—in nature, in technology, and even inside your own body!

Key Principle:  Energy cannot be created or destroyed—only converted from one form to another.
This is the Law of Conservation of Energy, one of the most fundamental ideas in all of science.

That means the total amount of energy stays the same—it just changes “clothes” as it moves through a system.

Why Do We Care About Energy Conversion?

Almost every device or natural process we rely on works by converting energy into a more useful form. But no conversion is 100% efficient—some energy always “escapes” as waste heat (usually thermal energy). Understanding these conversions helps us be more energy efficient.

Real-World Examples of Energy Conversion

Let’s explore how energy transforms in everyday situations:

1. Car Engine: Chemical → Thermal → Mechanical (+ Waste Heat)
   • Gasoline contains chemical energy stored in its molecular bonds.
   • When ignited in the engine, it burns (combustion), releasing thermal energy (heat).
   • The hot, expanding gases push pistons → creating mechanical (kinetic) energy to turn the wheels.
   • But… About 60–70% of the energy is lost as waste heat through the exhaust and radiator!
2. Television: Electrical → Light + Sound + Heat
   • When you plug in your TV, electrical energy flows into it.
   • This powers:
     • Light energy (pixels on the screen),
     • Sound energy (speakers vibrating air),
     • And thermal energy (your TV gets warm after hours of use—waste heat!).
   • Even “off” TVs in standby mode use a tiny bit of electricity—called vampire energy!
3. Incandescent Light Bulb: Electrical → Light + Heat
   • Only about 10% of the electrical energy becomes visible light.
   • The other 90% is “wasted” as heat—which is why these bulbs are being phased out.
   • LED bulbs are far better: they convert ~90% of electricity into light, with minimal heat!
4. Human Body: Chemical → Mechanical + Thermal
   • The glucose in your food stores chemical energy.
   • During cellular respiration, your cells convert it into:
     • Mechanical energy (to move muscles, blink, type, walk),
     • Thermal energy (to keep your body at 98.6°F / 37°C),
     • And even electrical energy (nerve signals in your brain!).
   • Efficiency? Only about 20–25% goes to useful work—the rest is heat (which is why you sweat when exercising!).
5. Hydroelectric Dam: Gravitational Potential → Kinetic → Mechanical → Electrical
   • Water held high behind a dam has gravitational potential energy.
   • When released, it falls → gaining kinetic energy.
   • Flowing water spins a turbine (mechanical energy).
   • The turbine turns a generator, producing electrical energy.
   • This clean, renewable process powers millions of homes—with very little waste!
6. Solar Panel: Radiant (Light) → Electrical
   • Photons from sunlight hit the solar panel.
   • Their energy knocks electrons loose in silicon atoms → creating an electric current.
   • This electrical energy can power your home, charge batteries, or feed into the grid.
   • No moving parts, no emissions—just pure energy conversion from the Sun!

Visualizing Energy Chains

Many systems involve multiple steps of conversion. Here’s a full chain:

Sun → (nuclear fusion) → Radiant energy → (photosynthesis) → Chemical energy in plants → (eaten by cow) → Chemical energy in milk → (you drink it) → Chemical energy in your body → (you pedal a bike) → Mechanical energy → (bike dynamo) → Electrical energy → (powers a headlight) → Light + Heat

One journey—from the core of the Sun to your bike light—through six forms of energy!

Final Thought: You’re an Energy Converter Too!

Every time you eat, move, think, or even breathe, you’re part of Earth’s grand energy cycle. By understanding how energy changes form, you become a smarter consumer, a more informed citizen, and a better problem-solver for the planet’s energy future.

Activity Idea:

Think about the energy conversions in your morning routine!

Example:

1. Alarm clock (electrical → sound)
2. Shower (chemical in gas → thermal)
3. Breakfast (chemical → body energy)
4. Bus ride (chemical → mechanical)

What other examples of energy conversions can you find in your morning routine? 

What Are Energy Sources?

In the last few pages, we talked about different forms of energy. But now we want to talk about the primary source of energy. Energy doesn’t just appear—it comes from sources found in nature. Some of these sources are limited, while others are constantly replenished. Scientists group them into two main categories:

• Renewable Energy Sources
• Nonrenewable Energy Sources

Understanding the difference helps us make smart choices about how we power our homes, schools, cars, and cities—now and in the future.

 The Big Difference: Can It Be Replenished?

 Renewable Energy Sources: Nature’s Endless Supply

Renewable energy comes from natural processes that are continuously renewed by the Earth or Sun. These sources won’t run out in our lifetime—or even in thousands of lifetimes!

1. Solar Energy

   • Comes from the Sun’s radiation.
   • Captured using solar panels (photovoltaic cells) or solar thermal systems.
   • Used for: Electricity, heating water, powering satellites.
   •  Clean, abundant, silent
   •  Intermittent (only works when sunny); needs storage (like batteries)

   Fun Fact: In just one hour, the Sun delivers more energy to Earth than humans use in an entire year!

2. Wind Energy
   • Uses moving air (kinetic energy) to spin turbine blades.
   • Turbines generate electricity.
   • Common in open plains, coastlines, and offshore.
   • No fuel, no emissions
   • Needs consistent wind; can affect birds
3. Hydropower (Water Energy)
   • Uses flowing or falling water (from rivers or dams) to spin turbines.
   • One of the oldest and most reliable renewable sources.
   • Highly efficient, can be stored (in reservoirs)
   • Dams can disrupt ecosystems and displace communities
4. Geothermal Energy
   • Taps into heat from deep inside the Earth (from radioactive decay and leftover formation heat).
   • Used to heat buildings or generate electricity (e.g., in Iceland or California).
   • Always available, small land footprint
   • Only practical in geologically active areas
5. Biomass
   • Organic material like wood, crop waste, or algae burned or converted to biofuels (e.g., ethanol).
   • Stores chemical energy from the Sun (via photosynthesis).
   • Renewable if sustainably grown
   • Burning biomass still releases CO₂ (though less than fossil fuels)

 Nonrenewable Energy Sources: Limited and Finite

Nonrenewable sources exist in fixed amounts. Once we extract and burn them, they’re gone for millions of years. Most of the world’s energy today still comes from these sources.

1. Fossil Fuels
   Formed over 300–400 million years from buried plants and microorganisms under intense heat and pressure. That’s why they’re called “fossil” fuels—they come from ancient life!

   • Coal: Solid fuel from ancient forests. Used mostly in power plants.
   • Oil (Petroleum): Liquid fuel refined into gasoline, diesel, and jet fuel.
   • Natural Gas: Gaseous fuel (mostly methane); burns cleaner than coal or oil.

    High energy density (great for transportation and industry)

    Major source of CO₂ emissions → climate change

   Causes air pollution (smog, acid rain)

    Fossil fuels are NOT evenly distributed:

   • Middle East: Rich in oil
   • USA, Russia, China: Large coal reserves
   • Russia, Iran, Qatar: Hold most natural gas
   • This uneven distribution affects global politics, trade, and conflict.

2. Nuclear Fission (Uranium)

   • Uses uranium-235, a rare metal mined from the Earth.
   • Atoms are split in a reactor, releasing huge heat → makes steam → generates electricity.
   • No CO₂ during operation; very high energy output
   • Produces radioactive waste that must be stored safely for thousands of years
   • Risk of accidents (e.g., Chernobyl, Fukushima)

    Important: While uranium is nonrenewable, a tiny amount produces massive energy—1 uranium pellet = 1 ton of coal!

 Energy Use in the United States (as of recent data)

• About 80% of U.S. energy comes from nonrenewable sources (oil, coal, natural gas, nuclear fission).
• About 20% comes from renewables—and this share is growing fast thanks to solar and wind.
• Transportation (cars, planes, trucks) relies heavily on oil—making it hard to decarbonize quickly, although electric vehicle use is quickly increasing.

 Why Concentration Matters: Solar vs. Oil

You might wonder: If the Sun gives us so much energy, why don’t we use it for everything?

The answer lies in energy density and concentration:

• Oil is a highly concentrated fuel. A single gallon contains enough chemical energy to drive a car 25+ miles.
• Sunlight, by contrast, is spread out. To match the energy in one barrel of oil, you’d need a large solar farm operating all day.

That’s why we often say:

“The problem isn’t the amount of solar energy—it’s capturing and storing it efficiently.”

Technologies like better batteries, smarter grids, and more efficient panels are solving this challenge every year!

Throughout this lesson, we’ve explored how energy is never created or destroyed—but constantly changes form. From the kinetic energy of a rolling skateboard to the thermal energy in a hot cup of cocoa, from the radiant light of the Sun to the nuclear energy deep inside atoms, energy is always moving, shifting, and making things happen.

One of the most important transformations we rely on every day is the conversion of chemical energy into mechanical energy. The food you eat stores chemical energy in molecules like glucose. Your body breaks those bonds and converts that stored energy into motion—allowing you to walk, write, play sports, or even blink! Similarly, when gasoline (a concentrated chemical fuel) burns in a car engine, it releases heat that pushes pistons, ultimately turning the wheels. In both cases—your muscles and your car—stored potential energy becomes active kinetic energy, powering movement and work.

We’ve also seen that where our energy comes from matters deeply. While fossil fuels like oil and coal have provided high-density chemical energy for over a century, they are nonrenewable and harm the environment. Renewable sources like solar, wind, and hydropower offer cleaner pathways—but they often require technology to convert their energy into usable forms like electricity or motion.

Understanding these conversions—and the sources behind them—empowers you to think critically about energy use. Every time you ride a bike, charge a phone, or flip a light switch, you’re part of a chain of energy transformations that began long ago, perhaps in ancient sunlight stored in plants or in the core of a distant star.

So remember:

Energy may be invisible—but its journey through our world is full of change, connection, and consequence. And now, you have the knowledge to see it, use it wisely, and help shape its future.

Welcome to Lesson 2!

In our last lesson, we explored the forms and sources of energy—from the chemical energy in your breakfast to the radiant energy streaming from the Sun. We learned that energy is the capacity to do work or produce heat, and that it can change forms but is never created or destroyed.

Now, we're adding a crucial piece to that foundation. Have you ever noticed that your phone battery drains faster when you're streaming video versus just texting? Or that a 13-watt LED light bulb uses electricity differently than a 100-watt bulb?

These everyday observations point to a key distinction that scientists, engineers, and even your utility company rely on:

Energy and Power are related, but they are not the same thing.

Think of it this way:

• Energy is the total amount of "fuel" you use—like the total gallons of gas put in your car this month.
• Power is the rate at which you use it—like how fast you burn that gas while accelerating onto the highway.

In physics terms:

Energy (measured in joules or kilowatt-hours) = how much work gets done

Power (measured in watts) = how fast that work happens

In this unit, we will be looking at how to convert energy and power units as well as reading electric bills. We will also learn how to calculate how much energy our household devices use and how much that costs us.

Lesson 2: Learning Objectives

By the end of this lesson, you'll see physics in action every time you flip a switch—and understand exactly what you're paying for when that bill arrives.

• Distinguish work, energy, and power using everyday examples
• Convert between units (joules ↔ kilowatt-hours) to connect physics class to your utility bill
• Calculate energy use: Energy = Power × Time (e.g., a 100 W bulb running 10 hours = 1 kWh)
• Interpret appliance labels to estimate real-world costs
• Decode an actual electricity bill—spotting how many kWh you used and why your cost per kWh isn't just the "supply rate"

In everyday life, we say we’re “working” when we study, carry groceries, or hold a heavy box. But in physics, the word work has a very specific meaning:

Work is done only when a force causes an object to move in the direction of the force.

That means three things must happen for work to occur:

1. A force must be applied.
2. The object must move (undergo displacement).
3. The motion must have a component in the direction of the force.

The Formula for Work

Where:

• Force is measured in newtons (N)
• Distance is measured in meters (m)
• θ (theta) is the angle between the force and the direction of motion
• Work is measured in joules (J) → 1 J = 1 N·m

But don’t worry—you don’t need trigonometry here. You may get in much more detail in a physics class, but not here. When force and motion are in the same direction (like pushing a shopping cart forward), cos(0°) = 1, so:

$\text{Work = Force × Distance}$

Real Examples of Work Being Done

• Pushing a stalled car 5 meters down the road → you apply force, and it moves → work is done.
• Lifting a backpack from the floor to your desk → you apply upward force against gravity, and it moves up → work is done.
• Pedaling a bike uphill → you push on the pedals, and the bike moves upward against gravity → work is done.

Common Situations Where NO Work Is Done (in physics terms!)

• Holding a heavy suitcase while standing still: You’re applying force (to counteract gravity), but there’s no displacement → zero work.
• Pushing hard against a wall that doesn’t move: Force? Yes. Motion? No → zero work.
• Carrying a box horizontally across a room: You apply upward force to hold it, but motion is horizontal. Since force (up) and motion (sideways) are perpendicular, no work is done against gravity. (You might get tired—but that’s biology, not physics!)

Units for Work: Joule (J), Calorie (cal), British Thermal Unity (BTU), kilowatt-hour (kWh), foot-pound (foot-lb)

Energy – The “Ability” to Do Work

If work is the act of moving something with force, then energy is what enables you to do that work. As we learned in the last lesson,

Energy is the capacity to do work.

Think of energy as your “work potential.” You can store it, transfer it, or convert it—but you can’t create or destroy it (thanks to the Law of Conservation of Energy).

For example:

• A raised hammer has gravitational potential energy → when dropped, it does work on a nail.
• A charged battery has chemical energy → it can do work to light a bulb or spin a motor.
• A moving soccer ball has kinetic energy → it can do work by knocking over a cup.

Energy Units: Joule (J), Calorie (cal), British Thermal Unity (BTU), kilowatt-hour (kWh), foot-pound (foot-lb)

**Note: Energy and Work have the same units!

Power: The rate at which we work (or energy) is done.

Now, imagine two people lift identical boxes to the same shelf:

• Person A does it in 2 seconds.
• Person B takes 10 seconds.

Both did the same amount of work (same force, same distance).
Both used the same amount of energy.
But Person A delivered more power.

Power is the rate at which work is done or energy is transferred.

 The Formula for Power

$\text{Power = }\frac{Work}{Time}\text{ = }\frac{Energy}{Time}$

• Measured in watts (W) → 1 W = 1 joule per second (J/s) 

  Bicycling Example

• Imagine two bicyclists pedal 10 miles uphill → same work, same energy (218 calories) **assuming the cyclists are approximately the same weight
• If Cyclist Y finishes in 30 minutes; while Cyclist Z the other finishes in 60 minutes
• The amount of energy used in both situation is the same, Cyclist’s Y power output is twice as high—not because he did more, but because he did it faster.
• Cyclist Y completed 10 miles in 30 minutes versus Cyclist Z 10 miles in 60 minutes

Common Units of Power: Watt (W), kilowatt (kW), horsepower (hp), British Thermal unit per hour (BTU/hr), Joule/sec (same as a Watt).

Energy, Work, and Power (3:33)

Why Unit Conversion Matters

You convert units all the time—often without even thinking about it!

• You know that 1 foot = 12 inches, so you can quickly figure out that 4 feet = 48 inches.
• You might also know that 1 yard = 3 feet, or that 1 mile = 5,280 feet.
• Maybe you’ve even heard that 1 mile ≈ 1.609 kilometers—useful when traveling or watching international sports!

When you’re familiar with the units, conversions feel easy. But what if you need to convert something less familiar—like miles to meters, gallons to liters, or joules to calories? That’s where a powerful tool comes in: the factor-label method.

What Is the Factor-Label Method?

The factor-label method (also called dimensional analysis) is a step-by-step strategy that lets you convert any unit to any other unit—as long as you know the right conversion factor.

The best part?
You never have to guess whether to multiply or divide!
The units themselves guide you.

How It Works: A Simple Example

Let’s convert 7.5 miles to feet.
We know: 1 mile = 5,280 feet

Step 1: Write down what you’re starting with

$\text{7.5 miles}$

Step 2: Multiply by a conversion factor written as a fraction

Choose the form that cancels the original unit (miles) and leaves the desired unit (feet):

$\text{7.5 miles × }\frac{\text{5,280 feet}}{\text{1 mile}}$

Notice how “miles” cancels out (one in the numerator, one in the denominator), leaving only feet.

$\text{7.5 }\cancel{\text{miles}}\text{ × }\frac{\text{5,280 feet}}{\text{1 }\cancel{\text{mile}}}$

Step 3: Do the math

$\text{75. × 5,280 = 39,600 feet}$

Why This Method Always Works

The key idea is this:

Any conversion factor is equal to 1—so multiplying by it doesn’t change the actual amount, just the units.

Since $\frac{5,280 \mathrm{ft}}{1 \mathrm{mi}}=1$, multiplying by it is like multiplying by 1—you’re just changing how you express the quantity.

This works for any unit:

• Time: seconds ↔ minutes ↔ hours
• Distance: inches ↔ cm ↔ meters ↔ km
• Energy: joules ↔ calories ↔ kilowatt-hours
• Mass: grams ↔ kilograms ↔ pounds

Pro Tips for Success

• Always write units—even in calculations. They’re your roadmap!
• Set up the fraction so the old unit cancels.
• Chain multiple steps if needed (like hours → minutes → seconds).
• Double-check: Does your answer make sense? (e.g., 7.5 miles should be many feet—not just 7!)

Final Thought

Once you master the factor-label method, no unit conversion will ever stump you again. Whether you’re solving physics problems, following a recipe, or planning a road trip abroad, this skill will serve you for life.

 Remember: Units are your friends. Let them guide you!

Want to see it in action?

Check out this helpful video tutorial:

Unit Conversion the Easy Way (6:14)

Now that we learned the factor label method for conversions, we can now try more complex conversions. Sometimes we need to convert several items in one problem.  We can do it the same, just follow the units.  

Example: Convert 55 mph to m/s

We want to change miles → meters and hours → seconds.

That means we need two conversion factors:

• 1 mile = 1,609 meters
• 1 hour = 3,600 seconds

Though it’s two changes, we use the same factor-label method—just with two fractions!

 Step-by-Step Using Factor-Label

Start with what you know:

$\text{55}\frac{\mathrm{miles}}{\mathrm{hour}}$

Step 1: Convert miles → meters

Use the fraction that cancels "miles":

$\text{55}\frac{\cancel{\mathrm{miles}}}{\mathrm{hour}}\text{×}\frac{1,609\mathrm{meters}}{1 \cancel{\mathrm{mile}}}$

→ "Miles" cancels out. Now we have meters/hour.

Step 2: Convert hours → seconds

We have “hours” in the denominator, so we need a fraction with “hours” on top to cancel it:

$\text{×}\frac{1 \mathrm{hour}}{3,600 \mathrm{seconds}}$

→ Now “hours” cancels too!

Put it all together:

$\text{55}\frac{\cancel{\mathrm{miles}}}{\cancel{\mathrm{hour}}}\text{×}\frac{1,609 \mathrm{meters}}{1 \cancel{\mathrm{mile}}}\text{×}\frac{1 \cancel{\mathrm{hour}}}{3,600 \mathrm{seconds}}$

Here's another way to look at it:

Now multiply the numbers:

$\frac{55\times 1,609}{3,600}=\frac{88,495}{3,600}\approx 2.46$

 Final answer: 55 mph ≈ 24.6 meters/second

 Key Tips for Multi-Step Conversions

1. Treat compound units (like mph) as two separate units:
   → “miles per hour” = miles ÷ hours, so convert numerator and denominator separately.
2. Always arrange conversion fractions so unwanted units cancel:
   • Want to cancel miles? Put miles in the denominator of your conversion factor.
   • Want to cancel hours? Put hours in the numerator.
3. You can chain as many steps as needed:
   Example: gallons → liters → milliliters → cm³ → m³… just keep adding fractions!

 Real-World Why It Matters

• Scientists and engineers always use metric units (like m/s), but speed limits are in mph in the U.S.
• Knowing how to convert helps you understand car safety data, physics problems, or even video game physics!
• 24.6 m/s is about how fast a major league fastball travels—so 55 mph is roughly fast-pitch softball speed!

 Quick Check: Does the answer make sense?

• 1 m/s ≈ 2.24 mph
• So 55 mph ÷ 2.24 ≈ 24.5 m/s → matches our result! 

When your estimate lines up, you know you’re on the right track.

Final Thought

Multi-step conversions might look intimidating at first—but with the factor-label method, you just add one fraction at a time, let the units cancel, and follow the math.

No memorizing “multiply or divide”—just let the units guide you!

Spot the Power Label!

Take a look around you right now. Chances are, you’re using a laptop, phone, or tablet—and it’s plugged into a charger. Flip that charger over (or look at the label), and you’ll likely see something like this:

Credit: Jennifer Clemons

Quick Check: Is Watt a unit of energy or power?

Remember from our earlier lesson:

• Power = how fast energy is used → measured in Watts (W)
• Energy = total amount used → measured in Watt-hours (Wh) or kilowatt-hours (kWh)

So Watt (W) is a unit of power—not energy!

Let’s Calculate: How Much Energy Does Your Laptop Use?

Suppose your laptop charger is rated at 65.0 W, and you use it for 10 hours each day.

$\text{Energy = Power × Time = 65.0 W × 10 hours = 650 Watt-hours }\left(\mathrm{Wh}\right)$

But utility bills don’t use Watt-hours—they use kilowatt-hours (kWh).

Since kilo = 1,000, we convert:

$\text{650 Wh × }\left(\frac{1 \mathrm{kWh}}{1,000 \mathrm{Wh}}\right)\text{ = 0.650 kWh}$

So your laptop uses 0.65 kWh per day.

What Does That Cost?

If we estimate electricity to cost about $0.15 per kWh (check your bill for your exact rate!).

$\text{0.65 kWh × \$0.15}/\text{kWh = \$0.0975 }\approx \text{ \$0.10 per day}$

That’s just 10 cents a day—or about $3 per month to run your laptop!

Depending on how much your electricity costs, you can now determine how much that one day of laptop use costs you each day (or month or year).

We will discuss appliances in more depth in a later lesson, but here is a list of common household appliances and their power ratings.  Again, they can vary greatly depending on the manufacturer and age.  Some appliances are getting significantly more efficient over time.   For the most up to date information, please check the manufacturers rating on the device you are interested in.  The table below is just an estimate. 
 

How electricity companies charge you

Have you ever looked at a utility bill? Really looked at the bill? More than just looking at the amount due. If you can, I would encourage you all to look at the bill to see some of the numbers on there. For this lesson, we are going to look at this utility bill. This is from PPL for June 2024.

At the top of the bill, you will see basic information, including:

• Account Number
• Due Date
• Amount Due
• Service Address
• Billing Period

In terms of this class, we really want to understand the usage. As we have already discussed, kWh (kilowatt-hour) is the basic unit of electricity and a unit of energy. This should be the unit on any electric bill might read. (You might see some additional units on there, including kW or BTUs, especially if your utility provides both electricity and natural gas service to your home.)

Total Usage: The amount of electricity (energy) used in the billing period. For the example bill it is 1,,434 kWh

Supply Charge versus Delivery Charge

This may be the most confusing part. This bill contains different charges for both Supply and Delivery. So what's the difference?

Supply Charge is for generating the electricity, typically from a power plant. In this example, the supply charge is $141.82 (which is the electricity usage 1,434kWh × $0.09890/kWh).

Unfortunately, that is not the only charge in this bill. Here we see a Delivery Charge. The Delivery charge is to maintain the poles and wires to deliver the electricity to your home. In this case, the Delivery Charge is $82.31, which includes all customer charges and distribution fees. You might be surprised to see the delivery charge is nearly 1/3 of the total bill. 

Depending on the provider, your bill may be more complicated or simpler than this bill. Not every utility separates out delivery and supply charges, however some companies may include additional charges like a demand charge.

So, looking at this example bill, what is the actual cost per kWh of usage?

$\text{\$224.14 total bill / 1,434 kWh = \$0.1563/kWh}$

This is much higher than the electric charge shown, because we included all the charges, taxes, and fees.

This bill also shows your usage over time. The chart on the first page of the bill shows the total electricity used between July 2023 and June 2024.   

Take a look at this bill and try and answer the following questions.  

• How much electricity was used in this time frame? (Answer: 12412 kWh)
• What is the average usage? (Answer: 1034 kWh)
• What month used the most electricity? (Answer: August)

Real-World Application

Your Turn: Grab your own (or a family member's) electricity bill and:

1. Circle the account number and due date
2. Calculate kWh used: (Current reading – Previous reading)
3. Find the split between supply vs. delivery charges
4. Note one thing that surprised you

Understanding your bill is the first step to managing energy costs wisely!

If you do not have access to an electric bill of your own, use this example electric bill from PPL Electric Utilities.

Basic Calculation

Your June bill shows:

• Supply charge: $90.00
• Delivery charge: $40.00
• Total kWh used: 875 kWh

Calculate:

Total bill = $90 + $40 = $130.00

Effective cost/kWh = $130 ÷ 875 = $0.1486/kWh

Compare Two Months

August (high usage): 1,500 kWh → $150 supply + $65 delivery = $215 total

September (low usage): 600 kWh → $75 supply + $30 delivery = $105 total

Calculate effective rates:

• August: $195 ÷ 1,500 = $0.130 /kWh
• September: $90 ÷ 600 = $0.150/kWh

Even with the same rates, September costs more per kWh because fixed delivery fees ($15–$20) get spread over fewer kWh.

Demand Charges Versus Energy Charges

We saw in an earlier part of this lesson the difference between energy and power.   For our electricity provider, our Energy use is how much kWh we use.   But we can also talk about the rate at which we use electricity, which is Power. 

For most homes, you only pay for energy (kWh). But businesses and some large facilities also pay a demand charge based on their highest power draw during the billing period. Why? Because the utility must build infrastructure (transformers, wires) sized for your peak demand not your average use.

Take for instance this example commercial bill.  It is also from PPL in June 2024, however it is much bigger than what most homeowners would pay for one month.   
PPL bill with demand charge: Commercial Bill 

On the Bill we can see the following: 

• Total Energy Used - 598,000 kWh
• Peak Demand - 1,095 kW
• Energy Charge         
• Demand Charge - $2.54701/ kW
• Days in Billing Cycle - 2
• Supply Charge $ - $0.00
• Delivery Charge - $3,133.19

In this case, the energy charge is negligible, but the customer paid a lot in their demand charge.   This customer could reduce their bill by reducing their electricity use when their draw is the highest.  Why?  Because the utility must build the infrastructure (wires and transformers) to account for your peak demand, not the average usage.

Time-of-Use Billing: 

Some utility bills use time-of-use (TOU) pricing, which charges different rates depending on the time of day you consume electricity—similar to "surge pricing" for rideshares or toll roads. During peak periods (typically 4 PM–9 PM on weekdays), rates are highest because demand on the grid spikes as people return home, cook dinner, and turn on appliances. During off-peak hours (usually 10 PM–6 AM), rates drop significantly due to much lower overall demand.

Why Peak Times Cost More

Electricity must be generated the instant it's used. When millions of households draw power simultaneously during evening hours, utilities must activate expensive "peaker" power plants to meet demand. TOU pricing reflects this real cost—and incentivizes customers to shift flexible loads to times when the grid has excess capacity.

Sample TOU Rate Structure

Hypothetical residential plan (rates vary by utility)

Smart Shifts That Save Money

Because peak rates can be 2 to 3 times higher than off-peak rates, small timing changes yield real savings:

Where TOU Is Common

TOU billing is increasingly standard in high-demand regions like California, Arizona, and parts of the Northeast—especially for customers with solar panels or electric vehicles. Always check your utility's specific peak windows, as they can shift seasonally (e.g., summer afternoons may become peak due to air conditioning demand).
 

You started this lesson distinguishing energy (the total "fuel" used) from power (how fast it's used). Now you can apply that knowledge to something you'll encounter for the rest of your life: your electricity bill.

In this lesson you learned to:

• Convert between physics units (joules) and billing units (kWh)
• Calculate appliance costs using Energy = Power × Time
• Decode a real bill—like identifying that 1,434 kWh used over 32 days equals a 45 kWh/day average
• Separate supply charges (the electricity itself, often shoppable) from delivery charges (grid maintenance, fixed by regulators)
• Recognize why your effective cost per kWh ($0.157 in our example) is higher than the supply rate alone ($0.099/kWh)—because delivery fees and fixed charges get added in

Most importantly, you now see physics not as abstract formulas, but as a lens for financial literacy. When you understand that a 1,500 W space heater running 4 hours costs about 6 kWh—and roughly 95¢ on a typical bill—you make smarter choices about energy use and costs.

This is energy literacy: the ability to translate classroom concepts into real-world decisions. Whether you're comparing electricity suppliers, sizing a solar panel system, or simply deciding whether to unplug that idle charger, the physics of energy and power puts you in control.

Welcome to Lesson 3!

Welcome to this exploration of world energy consumption. In 2024, humanity used approximately 186,000 terawatt-hours of energy that's enough to power every home, factory, vehicle, and data center on Earth. But where does this energy come from? How has our relationship with energy evolved since the days of wood fires? And what choices will determine whether we meet growing demand while protecting our climate?

In this lesson, we will be learning about the changes in energy supply and demand throughout history. We will be looking at both U.S. energy use and world energy use to understand patterns at multiple scales. While there are lots of numbers in this unit, it is important for us to remember trends and estimates, and not worry about the exact values. Energy data is complex and constantly updated—for example, the most recent energy data is available from the EIA U.S. Energy Facts Explained.

To illustrate this approach: In the latest U.S. data, we see that about 9% of U.S. energy comes from renewable sources. But what's most important to remember isn't the precise percentage—it's the bigger picture: petroleum and natural gas are the primary sources of U.S. energy use, and together those two sources account for nearly 75% of total U.S. energy consumption. That trend—fossil fuel dominance with renewables gradually growing—is the key takeaway.

Lesson 3: Learning Objectives

Upon completing this lesson, you should be able to:

• Analyze historical trends to understand how the Industrial Revolution transformed global energy use
• Compare energy consumption patterns across countries and connect them to GDP, geography, and lifestyle
• Investigate interactive data visualizations to see how fossil fuels still dominate—and how renewables are rising
• Evaluate three potential energy futures from the International Energy Agency and consider what "Net Zero" really means
• Calculate real-world applications like energy doubling time to grasp the scale of future demand

By the end, you'll not only understand the numbers behind global energy you'll be equipped to think critically about the policies, technologies, and personal choices that will power our shared future. Let's begin.

In 2024, the world wide energy consumption was about 186,000 TWhs (or 635 Quadrillion BTUs). The energy mix used by the whole world is shown below in the figure from Our World in Data. This figure is interactive, so you can slide the bar across and see how that information changes over time. The largest energy source for the whole world is Oil, followed by Natural Gas and Coal. This means most of the world's energy comes from fossil fuels. If you slide the bar around, you can see how renewable has begun to steadily increase in the past decade or more.

Energy consumption numbers are always reported a few years behind, so we are always looking into the past before we plan for the future. As of 2024, the world's total primary energy consumption was about 186,000 TWhs (635 Quadrillion Btus).

$${\text{TWh = Terrawatt-hour Terra means 10}}^{\text{12}}$$

$${\text{Quadrillion BTU = 10}}^{\text{15}}\text{ BTU}$$

What is interesting to see in this chart, which goes all the way back to 1800, is that for the first 100 years, the main energy source was only biomass and relatively consistent. In that time, nearly all energy was from biomass in the form of wood.  Do you know what happened in the late 1800’s to start the exponential growth of energy use? 

The Industrial Revolution played a key role in human development and energy use. Some inventions in that time period include:

• Steam Engine- allowed for travel and transportation of goods 
• Discovery of Oil- Titusville PA 1859
• Textile Machinery 
• Internal Combustion Engine 
• Electric Generator 
• Electric Lighting 

After the industrial revolution, we start to see an increase in coal use, followed by oil and finally natural gas.   Recall from lesson 1, those three energy sources are called our Fossil Fuels.  Those three energy sources also account for the majority (over 80%) of the world’s energy use. 

Please use the interactive features of this figure (using the arrow next to the year 1800) to adjust the time frame and investigate this chart further. 

The figure below shows how energy use is used per person (or per capita). You can see which countries have the highest energy use per person, in the dark red. The US is one of the highest consumers (but not the highest). Which country do you think is the highest user of energy per capita?

You can also explore this data, to see how it has changed over time. One major change over time is with China, which starts the time-laspe as about 1,000 kWh/ per person and ends the time-lapse at over 30,000kWh/per person.

• Do you expect this number to steadily increase?
• What do you expect to happen to India in the next 10 years?
• Do you think US energy use has increased, decreased or stayed the same over time?

Please click on the "Explore the data" for more analysis of each country over time.

According to the International Energy Agency, the world energy outlook for 2025.  This report is modeling three different potential energy futures, Current Policies Scenario, State Policies Scenario and Net Zero Emissions Scenario.  Those three scenarios are shown below. 

Three Scenarios, Three Futures

Please take a look at the World Energy Outlook 2025 Executive Summary of this latest report.  

Key takeaways include: 

• Energy demand is expected to grow through 2050, but that rate depends on the speed of which India and Southeast Asia grow. 
• While coal will continue to decline, natural gas and petroleum and still expected to grow throughout the mid-century.  Coal use is expected to peak somewhere around 2030. 
• Global temperatures will continue to increase, expected to reach 3°C by 2100 if current policies remain.  Under the Net Zero Emissions Scenario we can still expect an increase in global temperature of 1.65°C
• Electrification plays a growing role worldwide.  Data Centers and AI account for 10% of world wide electricity consumption, however the US sees a larger share of these centers. 

Nearly 9% of the world population still live without electricity, and nearly 2 billion people rely on polluting cooking methods such as open fires and charcoal. 

Podcast: World Energy Outlook

The figure below shows the per capita energy consumption for each country. The energy sources are also split out by source, so you can see where each country gets their energy. The US consumes the most energy per person. Interact with the graph and answer the following questions.

• What country is #2 energy consumer per capita?
• What is the average energy consumption per capita for the average citizen of the world?
• What source of energy is the highest for a citizen of China?
• In 1965, which country was the second largest energy consumer in the world?

The figure below shows the Global Primary energy consumption by source. This shows how the world wide energy sources have changed over time. As you explore the data, answer the following questions.

• What was the primary world-wide energy source prior to 1860s?
• What is the primary world-wide energy source today?
• In what year do you see Nuclear become an energy source?
• What renewable energy source is the largest percentage of world-wide energy?

Energy Consumption and Electricity Projections

According to the International Energy Outlook (2023), global electricity generation will increase through 2025, however most of generation will be produced from renewable (zero-carbon) technologies. It is important to note that Net-Zero Carbon technologies are renewables, however, it can include nuclear power. Nuclear power plants do not emit any carbon emissions, so the figures below include nuclear as well as renewables. There has been increased discussion about nuclear power in recent years, including Small Modular Reactors (SMR), so it is possible to see a resurgence of nuclear power in the next 10-20 years.

In the IEA 2023 report, the combined share of fossil fuels (coal, petroleum and natural gas) is expected to decrease. They also predict that electric vehicles are expected to account for 29%-54% of all new vehicles sales by 2050. China and Western Europe are leading the switch to Electric Vehicles.

You can see in the figures below that the EIA predicts that world-wide electricity generation is expected to increase anywhere between 30-76% through 2050. The gray shaded area on the charts represents the level of uncertainty in development depending on a number of policy and economic factors. Renewables and nuclear are expected to produce most of the world’s electricity needs through 2050.

Text description of the World Electricity Generation by Fuel Type image.

The image displays six line graphs representing global electricity generation projections by fuel type, measured in billion kilowatthours, from 2020 to 2050. The graphs include total electricity generation, coal, solar, natural gas, wind, and nuclear. Each graph features a black line depicting the reference scenario and a shaded area indicating projection uncertainty. The total electricity generation graph shows a steady increase. Coal remains relatively stable, while solar shows substantial growth. Natural gas and nuclear exhibit slight increases, and wind shows moderate growth. The top right corner features the EIA logo.

Credit: U.S. Energy Information Administration, International Energy Outlook 2023

The figure below shows the expected electricity generation through 2050 from different areas of the world. China is expected to grow in all electricity generation, including fossil fuels, however their zero-carbon technologies are expected to account for most of their electricity generation through 2050. They are projected to have rapid growth in renewables through 2030 and start to level off as we get closer to 2050. Western Europe is expected to see nearly all of their increase in electricity generation to come from zero-carbon sources, while fossil fuel generation is decreasing. India shows a dramatic increase in electricity production from net zero-carbon sources, while fossil fuels remain plateaued through 2050. Africa shows an increase in electricity generation from all sources through 2050.

Text description of the electricity-generating capacity image.

The image is a multi-panel chart depicting projected electricity-generating capacity for zero-carbon and fossil fuel-based technologies across four different regions: China, Western Europe, India, and Africa, from 2020 to 2050. Each panel contains line graphs representing both types of technologies with area shading to show range variations.

1. China - The graph shows a significant increase in zero-carbon technologies, represented by a blue line and shaded area expanding upwards from 2020 to 2050. The fossil fuel-based technologies, shown in black, remain relatively stable.
2. Western Europe - The graph shows a moderate rise in zero-carbon technologies, with fossil fuel-based ones remaining relatively constant, similar to China's panel.
3. India - The blue line for zero-carbon technologies shows strong growth, indicating a rising trend. Fossil fuel-based technologies shown in black remain mostly flat.
4. Africa - Both zero-carbon technologies and fossil fuel-based technologies are projected to rise, but zero-carbon technologies are expected to increase at a faster rate.

Credit: U.S. Energy Information Administration, International Energy Outlook 2023

Future energy use:

While no one has a crystal ball to predict where our future energy use may come from, estimates from both the EIA and IEA expect energy use to grow in the future. Most of this new electricity/energy production is expected to come from renewable or net-carbon zero sources.

 

For a long time, growth in the world and the U. S. energy consumption as a function of time, follow what is known as exponential function. Now it looks like we have switched to linear growth, but time will tell if this is a permanent change. The exponential increase is characterized as follows. The amount of change (increase in energy consumption) per unit time is proportional to the quantity (or consumption) at that time.

We can determine how long it takes for N₀ to become 2N₀ (twice its original number or double). That time period is called doubling time. After some mathematical steps it can be written as:

$$\mathbf{\text{Doubling Time = 70 / \% Growth Rate per Year}}$$

Fossil Fuels account for a large portion of the world's energy sources. These fossil fuels are non-renewable fuels with a finite lifetime. So, the question is: Will we have enough supply for future energy requirements?

The answer to this question depends on the quantity of fossil fuels we have in the ground. Energy sources that have been discovered but not produced cannot be easily measured. Trapped several feet below the surface, they cannot be measured with precision. There are several terms used to report the estimates of the energy resources. The most commonly used terms are “reserves” and “resources.”

• "Reserves" represent that portion of demonstrated resources that can be recovered economically with the application of extraction technology available currently or in the foreseeable future. Reserves include only recoverable energy.
• “Resources” represent that portion of the energy that is known to exist or even suspected to exist, irrespective of technical or economic viability. So reserves are a subset of resources.

Coal

While much of the world has decreased their use of coal over the past two decades, both China and India have been increasing their use of coal.   Push the play button below to show how coal usage has changed since 1900.   The US was the #1 producer of coal until the 1980s, when China became #1.   Since then, China's coal production has continued to increase with the exception of a small dip during COVID. 

As of 2025, total world proved recoverable reserves of coal were estimated at 1139 billion short tons. In many countries, such as the US, coal consumption has been decreasing. However, in China and India, coal use has increased significantly in the past decade.

Five countries have nearly 73% of the world's coal reserves:

• United States—28%
• Russia—18%
• China—13%
• Australia—9%
• India—7%

Petroluem

Based on data from OPEC (Oil Producing and Exporting Countries), the highest proved oil reserves including non-conventional oil deposits are shown in the graphic below. This shows which regions of the world have the highes amounts of oil reserves. You can interact with this figure to show the historical change of proven reserves or create different types of charts to separate by country.

The top countries for oil resereves are Venezuela, Saudia Arabia, Canada Iran and Iraq. The US does have considerable about of oil resources and lands in the top 10 of oil producing countries.

Based on data from BP (British Petroleum), proved gas reserves were dominated by three countries: Russia, Iran and Qatar, which together held nearly half the world's proven reserves. According to the US CIA The World Factbook, the US has the 4th largest reserves of natural gas. Due to constant updates about the shale gas estimates, these are difficult to say with certainty.

How Long Will the Reserves Last?

How long these reserves do last depends on the rate at which we consume these reserves. For example, let’s assume that we have $100,000 in the bank (reserves) and if we draw 10,000 dollars every year (consumption) the reserve will last for 10 years (\$100,000/\$10,000 per year). However, in this case, we are assuming that we do not add any money to our deposit, and we do not increase our withdrawal.

This is generally not true in the case of life of an energy reserve. We may find new reserves, and our energy consumption or production can also increase. In the case of energy reserve, although we know that we might find new resources, we do not know how much we could find. But the consumption can be predicted with some accuracy based on the past rates.

Lifetime of current reserves at constant consumption

We can calculate the life of current petroleum reserves by dividing the current reserves by current consumption.

• At the current rate of consumption, the approximate lifetime of the world’s petroleum, natural gas, and coal reserves is 47.1 years, 52.4 years, and 133 years, respectively.
• At the current rate of consumption, the current U. S. petroleum, natural gas, and coal reserves will last approximately for 6.3 years, 21.5 years, and 919 years, respectively.

It is important to note that the entire U.S. petroleum consumption is not coming from the U.S. reserves because we import more than one half of the consumption. Because we import more than one half of the consumption, the petroleum reserves at the current rate will last about 11 years. If the consumption increases in the future, the life will be less. However, there is also a chance of adding more reserves with more exploration and discoveries. The increase in consumption can change depending on the price of petroleum and other alternative fuels. Likewise, us moving to electric cars and harnessing unconventional oil reserves can extend the lifetime of these reserves.

Therefore, these lifetimes are not carved in stone. It can be debated whether the U.S. reserves will last for 6 years or 10 years or even 20 years, or we may never run out! But there is increasing consensus that we must change our lifestyle. Even if we won't run out, the environmental consequences of continued use are pushing us to change anyway, but more on that later...

The R/P ratio can change from year to year, similar to our bank balance. We can add more if we make more or consume more. That changes the time we can draw on the balance.

Therefore, we must conserve, innovate (get more with less), or learn to live without these resources.

The current energy use in the US can be easily found by accessing the EIA US energy Facts Explained. Below there is some discussion about energy use in the US.  While the values may change slightly from year to year, it is important to remember the trends and rough estimates for the values.  For example, the latest chart from EIA might have renewables at 8.24 Quads and Petroleum at 38%.  You will not be expected to remember the actual number, but roughly the amount.  In the latest values from EIA, petroleum and natural gas account for 74% of the US’s total energy use.  If we include coal, the fossil fuels account for over 80% of US energy use. 

The chart below is a Sankey Diagram. This allows us to see where all of our energy use in the US is going.   If we follow the blue box for Natural Gas, we can see we start with 33.4 Quads of Natural Gas.   From that, 13.3 Quads of Natural Gas is used for Electricity Generation.    Small amounts of Natural Gas go to Residential (home heating), Commercial and Industrial uses.   Even a small amount of natural gas goes to transportation, which we will discuss more in lesson 12.   

 But lets go back to the Electricity Generation Block in orange. We can see a total of 32 Quads of energy goes into Electricity Generation.   This comes from a variety of sources, actually a little bit from every sources on the left hand side.    Of that 32 Quads coming into the Electricity generation, only 13.3 Quads leaves as electricity.  Where does the rest of that energy go?   Follow the Gray line to the right hand side.

Are you surprised?  Of all the energy used in the US, approximate 65% of this is Rejected Energy!  Only about 35% of our energy consumption in the US goes to useful energy use.  We will discuss why in Lesson 4 on energy efficiency. 

Image description: Estimated U.S. Energy Consumption in 2023

The image is a Sankey diagram illustrating the estimated U.S. energy consumption in 2023, totaling 93.6 quadrillion BTUs (Quads). It shows the flow of energy from various sources to different sectors and highlights the amount of energy that is ultimately rejected or used. Energy sources are color-coded and include solar (yellow, 0.89 Quads), nuclear (red, 8.1 Quads), hydro (blue, 0.82 Quads), wind (purple, 1.5 Quads), geothermal (brown, 0.12 Quads), natural gas (light blue, 33.4 Quads), coal (gray, 8.17 Quads), biomass (light green, 5 Quads), and petroleum (dark green, 35.4 Quads). The energy flows into categories such as electricity generation (orange, 32 Quads), residential (pink, 11.3 Quads), commercial (pink, 9.3 Quads), industrial (pink, 26.1 Quads), and transportation (dark green, 28 Quads). Finally, the diagram shows rejected energy (gray, 61.5 Quads) and energy services (gray, 32.1 Quads). The logo of Lawrence Livermore National Laboratory is in the top right corner.

[Transcribed text]

Source: LLNL October, 2024. Data is based on DOE/EIA SEDS (2024). If this information or a reproduction of it is used, credit must be given to the Lawrence Livermore National Laboratory and the Department of Energy, under whose auspices the work was performed. Distributed electricity represents only retail electricity sales and does not include self-generation. EIA reports consumption of renewable resources (i.e., hydro, wind, geothermal and solar) for electricity in BTU-equivalent values by assuming a typical fossil fuel plant heat rate. The efficiency of electricity production is calculated as the total retail electricity delivered divided by the primary energy input into electricity generation. End use efficiency is estimated as 65% for the residential sector, 65% for the commercial sector, 49% for the industrial sector, and 21% for the transportation sector. Totals may not equal sum of components due to independent rounding. LLNL-MI-410527

Source: Lawrence Livermore National Laboratory (LLNL): Energy Flow Charts

Fossil Fuels

Fossil Fuels still remain a major component of energy use in the US. As shown in the figure above, over 80% of US energy use is produced from fossil fuels.  The three fossil fuels are coal, oil and natural gas.

As a result of innovations in oil and gas extraction, U.S. imports have dropped considerably. While the US still consumes a lot of oil for transportation, a lot more oil has been discovered and produced domestically.

Image description: U.S. energy net imports by major source, 1950-2023

The image is a line graph titled "U.S. energy net imports by major source, 1950-2023," measured in quadrillion British thermal units. The horizontal axis represents the years from 1950 to 2023, while the vertical axis measures energy quantities ranging from -10 to 25 quadrillion British thermal units. There are four colored lines, each representing a different energy source. The brown line shows crude oil imports, peaking around 2005 at over 15 units before declining to approximately 2 units by 2023. The maroon line indicates petroleum products, with fluctuations around 5 to 10 units until it declines to negative values in recent years. The blue line for natural gas remains relatively stable from the 1970s, eventually dipping below zero after 2000. The black line represents coal and coal coke, consistently near zero, slightly fluctuating around the mid-20th century. Each energy source is identified with corresponding colors in the legend below the graph. At the bottom left, the "eia" logo is visible, along with a text box citing the data source.

Credit: EIA Energy Explained

Looking at the U.S. Energy Profile, It can be seen from the imports profile that the US Crude oil imports have significantly reduced between 2005 and 2019 from a peak of 25 Quadrillion BTUs. Another significant change that can be noted is that the US is now exporting natural gas (below zero on the y axis) instead of importing it. Although crude oil is imported, US exports finished petroleum products resulting in less net imports. As a matter of fact, US total energy exports exceeded the imports in 2019 since 1950.

The top five countries (sources) of US total petroleum in 2019 were Canada (49%), Mexico (7%), Saudi Arabia (6%), Russia (6%) and Columbia (4%).

The U.S. also ranks:

• first in worldwide reserves of coal;
• sixth in worldwide reserves of natural gas;
• eleventh in worldwide reserves of oil.

US Energy Consumption by Source and the chart of the US Energy consumption by source and user sector shows each energy source and the amount of energy it supplies in British thermal units (BTU). Petroleum is the leading source of energy in the US in 2019 with 36.72 quadrillion BTUs. Next is natural gas with 32.10 quadrillion BTUs. Coal supplies 11.31 quadrillion BTUs of energy. Renewable energy and nuclear power are responsible for 11.46 and 8.46 quadrillion BTUs respectively. Of the total petroleum consumption, 72% is used for transportation and another 23% is used by the industrial sector. Similarly, 35% of the natural gas (largest fraction) is used for power generation. On the other hand, 76% of the residential and commercial energy needs are met by natural gas. The actual percentages are not required to be memorized but answers to the questions such as: Which fuel is most used by power plants for power generation? Which sector uses petroleum the most? Approximately what fraction of the electricity is generated by renewable energy? (10, 25, 50 or 90) What is the primary purpose of coal use? etc. need to be answered.

US Energy Consumption by Source and Sector

The graph shows how dependent the U.S. is on our petroleum supply, as it accounts for almost 37% of our energy. Our next two highest sources of energy, like petroleum, are non-renewable and include natural gas and coal. Only about 11% of our energy comes from renewable energy sources such as wood and water (hydroelectricity). According to Energy Information Administration, US renewable energy consumption surpassed coal for the first time in over 130 years in 2019. Of the 4.12 trillion kWh of electricity generated in the US, 38% was from natural gas, coal accounted for about 23% and nuclear adding another 20%. Renewable sources contributed to 17% of the total electricity generated.

Image description: U.S. Energy Consumption by Source and Sector, 2024

The flow diagram illustrates the U.S. energy consumption by source and sector for the year 2024, measured in quadrillion British thermal units (Btu). On the left, the energy sources are listed with corresponding percentages: petroleum (35.3, 38%), natural gas (34.2, 36%), renewable energy (8.6, 9%), nuclear (8.2, 9%), and coal (7.9, 8%), totaling 94.2 quadrillion Btu. The lines connect these sources to various end-use sectors on the right: transportation (28.1, 38%), industrial (26.1, 35%), residential (11.2, 15%), and commercial (9.5, 13%) with a total of 74.9 quadrillion Btu. In the center, a section is dedicated to the electric power sector, splitting into electricity sales (13.5, 41%) and energy losses (19.3, 59%), with a total of 32.8 quadrillion Btu. Different colored lines represent energy flow from each source to sectors, indicating the percentage allocation.

Credit: Energy Review Monthly, April, 2025 by EIA

In 2023, fossil fuels made up 84% of total U.S. energy consumption, the lowest fossil fuel share. The greatest growth in renewables over the past decade has been in solar and wind electricity generation. Liquid biofuels have also increased in recent years, contributing to the growing renewable share of total energy consumption. 2020 was the first year that renewables surpassed coal consumption in the U.S.

US Energy Consumption Over Time

Image description: U.S. Primary Energy Consumption

The image is a line graph displaying energy consumption trends in the United States from 1950 to 2024, measured in quadrillion British thermal units (Btu). The horizontal axis represents years from 1950 to 2024, while the vertical axis represents energy consumption in quadrillion Btu, ranging from 0 to 50. Five colored lines represent different energy sources. The green line indicates petroleum consumption peaking around 40 quadrillion Btu in the early 2000s. The brown line, representing natural gas consumption, steadily rises, nearly intersecting petroleum consumption in 2020 and again in 2024. The blue line shows coal consumption, peaking around 1990 but sharply declining thereafter. The red line, depicting total renewable energy consumption, shows a gradual increase. The yellow line, representing nuclear electric power, rises sharply around 1970 and stabilizes. A legend at the bottom specifies the color coding for each energy type.

Credit: US EIA, Energy Monthly Review Apr. 2025

The most significant decline in recent years has been coal: US energy consumption from coal was at a high of 37% in 1950 to only 9% in 2023. Biomass, which includes wood as well as liquid biofuels like ethanol and biodiesel, remain relatively flat, as wood use declines and biofuel use increases slightly. In contrast, wind and solar are among the fastest-growing energy sources in the projection, ultimately surpassing biomass and nuclear.

US Energy Consumption History

The plot of US energy consumption shows the relative amounts of each type of energy that was consumed for each year. The history of the energy consumption profile of the United States indicates that petroleum makes the largest part of the energy demand over the past seven decades. Natural gas has taken the second over the past decade with the production of gas from shale. Coal has been replaced by renewable energy and natural gas for electricity generation. Among the renewable energy sources, biomass has the larger share followed by wind energy. Wind energy and solar energy are the fastest growing energy sources.

Credit: US EIA

Credit: EIA Annual Energy Outlook 2021

Answers to the following questions need to be looked for in the material presented above.

• Of all the renewable energy sources, which renewable source is used most?
• Which of the renewable sources is used most for transportation?
• Approximately what fraction of the electricity is generated by nuclear energy? (10, 20, 50 or 90)

Electricity

Electricity demand is expected to grow in the future. Visit the webpage US electricity explained - Sources and profiles

Examine for:

• Sources of U.S. electricity generation
• What are the notable changes in the major sources for electricity generation between 1950 and today?
• Role of renewable energy in the electricity generation.

Growth in electricity use for in the residential and commercial sectors is partially offset by improved efficiency. However, increases in demand from electric cars and data centers are causing a expected increase in electric demand. In 2023, Fossil Fuels accounted for 60% of US electricity generation, with natural gas accounting for most of that.  

Most capacity additions over the next 10 years are expected to be renewables.

Lesson 3 Review

Throughout this lesson, we've traced humanity's energy journey: from biomass-dependent societies before 1800, through the fossil-fueled explosion of the Industrial Revolution, to today's complex global system where over 80% of energy still comes from oil, coal, and natural gas. We've seen how energy use per person varies dramatically by country—and how factors like efficiency, climate, economic structure, and policy shape those differences far more than income alone.

Most importantly, we've looked ahead. The International Energy Agency presents us with three distinct pathways:

• Current Policies: ~3°C warming by 2100
• Stated Policies: ~2.5°C warming if promises are kept
• Net Zero by 2050: Limiting warming to ~1.65°C through rapid clean energy transition

The data is clear: global energy demand will continue to rise, especially in developing economies. But how we meet that demand is the defining question of our century. Renewable energy and electrification are accelerating. Nuclear power is being reconsidered. Efficiency gains offer immediate impact. And every nation—and every individual—has a role to play.

Your takeaway: Understanding energy isn't just about memorizing statistics. It's about recognizing connections—between history and innovation, between policy and personal choice, between today's consumption and tomorrow's climate. As you move forward, keep asking: What kind of energy future do we want to create—and what will it take to get there?

Welcome to Lesson 4!

Every day, we rely on devices that convert energy from one form to another: your phone transforms electrical energy into light and sound, a car engine turns chemical energy from gasoline into motion, and a power plant converts heat from fuel or fission into the electricity that powers your dorm. But here's a critical question: how much of the original energy actually does the work we want? The answer lies in the concept of energy efficiency—a measure of how well a system converts input energy into useful output. In this lesson, we'll explore why no conversion is perfect, especially when thermal energy (the random motion of molecules) is involved, and how fundamental laws of physics set hard limits on what engineers can achieve.

In this lessons, we will look at the operating principle of a heat engine. A heat engine is a device that converts heat to work. Particularly, automobiles are all heat engines, and they are notoriously inefficient. We will see examples and calculations of why these automobiles are notoriously inefficient and learn how to calculate the theoretical maximum efficiency of any heat engine using the Carnot efficiency.  For these calculations, we must make sure our temperatures are in the Kelvin, an absolute temperature scale. 

We can also calculate the efficiency of a whole process from the step efficiencies. For example, if it involves 2 or 3 steps like in a relay race. You know you have 3 or 4 players taking the baton and one lap by each of the athletes. So, what is the overall or team efficiency if we know the efficiency of each of those steps or the efficiency of each of those players? This multiplicative effect explains why small improvements at each stage can lead to big gains in total performance—and why understanding these principles is essential for designing sustainable, high-performance technology. By the end of this lesson, you'll be able to analyze energy systems critically and appreciate why efficiency isn't just a number—it's a bridge between physics and the future of energy.

Lesson 4: Learning Objectives

Upon completing this lesson, you should be able to:

• define and calculate efficiency of an energy conversion device;
• explain why energy conversion devices cannot achieve 100% efficiency 
• convert temperatures between Celsius and Kelvin;
• explain operating principles of a heat engine; and
• calculate overall efficiency from step efficiencies.

See the calendar in Canvas for due dates/times.

Questions?

If you have any questions, please post them to the General Course Questions forum in located in the Discussions tab in Canvas. I will check that discussion forum daily to respond. While you are visiting the discussion board, feel free to post your own responses to questions posted by others - this way, you might help a classmate!

In the first lesson, we saw that energy can be transformed from one form to another, and during this conversion, all the energy that we put into a device comes out. However, all the energy that we put in may not come out in a useful form.

For example, we put electrical energy into a bulb and the bulb produces light (which is the desired form of output from a bulb), but we also get heat from the bulb (undesired form of energy from an electric bulb).

Text description of the Electrical energy conversion to light and heat image.

The image shows a chalkboard with a diagram illustrating the transformation of electrical energy. On the left side, the words "Electrical Energy" are written in yellow chalk. An arrow points right to a simple outline of a light bulb in the center, suggesting the conversion process. Two arrows extend from the light bulb to the right, each labeled; the upper arrow points to the word "Light," and the lower arrow points to "Heat."

Credit: © Penn State is licensed under CC BY-NC-SA 4.0

Therefore, energy flow into and out of any energy conversion device can be summarized in the diagram below:

Text description of the Energy Flow Diagram for an Energy Conversion Device image.

The image is a diagram on a dark gray background resembling a chalkboard. The left side of the image shows the words "Energy Input" with an arrow that points towards a large rectangular box labeled "Energy Conversion Device."  From the right side of the box, two arrows extend; one labeled "Useful Energy Output," and the other labeled "Energy Dissipated to the Surroundings."

Credit: © Penn State is licensed under CC BY-NC-SA 4.0

When all forms of energy coming out of an energy conversion device are added up, it will be equal to the energy that is put into a device. Energy output must be equal to the input. This means that energy can not be destroyed or created. It can only change its form.

In the case of an electric bulb, the electrical energy is converted to light and heat.

Self Check

Instructions: Identify the useful energy output(s) and undesirable energy output(s) in the energy conversion devices below. Enter your answers in the fields provided, and click the "Check" button to check your work.

Efficiency is the useful output of energy. We can mathematically define energy efficiency as the ratio of useful energy output to total energy output. This will give us a value between 0-1. To get this as a percentage, you should multiply by 100%. To calculate efficiency, the following formula can be used:

$$\text{Efficiency}=\frac{\text{Useful\hspace{0.17em}Energy\hspace{0.17em}Output}}{\text{Total\hspace{0.17em}Energy\hspace{0.17em}Output}}\times 100\%$$

This simple yet powerful equation allows us to express efficiency as a percentage, where 100% would represent a theoretically perfect device with no energy losses—a condition that, as we will explore, is impossible to achieve in practice due to the fundamental laws of thermodynamics.

NOTE: You can never have energy efficiency over 100%. If you get a value above 1 by using the formula above, make sure you have the USEFUL energy value on the top and TOTAL energy output on the bottom of the equation.

What if the units are not the same? You need to have the same units in order to determine efficiency.

Energy Efficiencies

Energy efficiencies are not 100%, and sometimes they are pretty low. The table below shows typical efficiencies of some of the devices that are used in day to day life:

From our discussion on national and global energy usage patterns in Lesson 3, we have seen that:

• about 41% of the US energy is used in power generation;
• about 38% of the US energy is used for transportation.

Yet the energy efficiency of a power plant is about 35%, and the efficiency of automobiles is about 25%. Thus, over 62% of the total primary energy in the U.S. is used in relatively inefficient conversion processes.

Why are power plant and automobile design engineers allowing this? Can they do better?

There are some natural limitations when converting energy from heat to work.

Thermal energy is energy associated with random motion of molecules. It is indicated by temperature, which is the measure of the relative warmth or coolness of an object.

A temperature scale is determined by choosing two reference temperatures and dividing the temperature difference between these two points into a certain number of degrees.

The two reference temperatures used for most common scales are the melting point of ice and the boiling point of water.

• On the Celsius temperature scale, or centigrade scale, the melting point is taken as 0°C and the boiling point as 100°C, with the difference between them being equal to 100 degrees.
• On the Fahrenheit temperature scale, the melting point is taken as 32°F and the boiling point as 212°F, with the difference between them being equal to 180 degrees.

It is important to realize, however, that the temperature of a substance is not a measure of its heat content, but rather, the average kinetic energy of its molecules resulting from their motions.

When water molecules freeze at 0°C, the molecules still have some energy compared to ice at -50°C. In both cases, the molecules are not moving, so there is no heat energy.

So what is the temperature at which all the molecules have absolutely zero energy? A temperature scale can be defined theoretically, for which zero degree corresponds to zero average kinetic energy. Such a point is called absolute zero, and such a scale is known as an absolute temperature scale. At absolute zero, the molecules do not have any energy.

The Kelvin temperature scale is an absolute scale having degrees the same size as those of the Celsius temperature scale. Therefore, all the temperature measurements related to energy measurements must be made on Kelvin scale.

Any device that converts thermal energy into mechanical energy—like a car engine, a jet turbine, or a coal-fired power plant—is called a heat engine. These machines work by taking in high-temperature heat (usually from burning fuel or nuclear reactions), using part of that energy to do useful work—such as turning wheels or generating electricity—and releasing the remaining energy as lower-temperature waste heat, often into the air or a nearby body of water. This "exhaust" isn't a flaw in engineering; it's a fundamental requirement of how nature works. Because heat naturally flows from hot to cold, a heat engine can only extract work while that flow is happening—and it can never capture all the energy in the process.

Text description of the Energy Conversions in an Automobile image.

The image is a blackboard with a diagram illustrating a process flow. Three rectangles are aligned horizontally across the board. The first rectangle on the left contains the text "Chemical Energy," the middle rectangle has the text "Thermal Energy," and the rectangle on the right displays "Mechanical Energy." Arrows connect the rectangles, showing a flow from left to right, indicating a progression from chemical to thermal to mechanical energy.

Credit: © Penn State is licensed under CC BY-NC-SA 4.0

This limitation is described by the Second Law of Thermodynamics, which tells us that no heat engine can be 100% efficient. Efficiency is defined as the ratio of useful work output to the total heat energy input, and it's fundamentally limited by the temperatures of the heat source and the environment. In fact, the maximum possible efficiency (called the Carnot efficiency) depends directly on the absolute temperatures—measured in Kelvin—of the hot and cold reservoirs: the bigger the temperature difference, the more work you can extract. For example, a car engine operating between ~1500 K (combustion) and ~300 K (outside air) has a theoretical maximum efficiency around 80%, but real-world factors like friction and incomplete combustion bring actual efficiency down to just 20–30%. Power plants, which can operate at more controlled high temperatures, often reach 35–60% efficiency.

Understanding heat engines helps explain why energy conservation matters and why engineers constantly seek better materials and designs. Waste heat isn't just "lost"—it affects fuel economy, emissions, and even local ecosystems when warm water is discharged from power plants. By studying these systems, you'll see how core scientific principles—like absolute temperature, energy conservation, and entropy—directly shape the technology that powers our world. As you move forward in physics or engineering, you'll learn to analyze these cycles quantitatively, but for now, remember this key idea: heat engines don't create energy; they redirect it, and nature always takes a share.

Text description of the Heat Engine image.

The image depicts a schematic diagram of a heat engine. It consists of a gradient background transitioning from red, labeled "High T" at the top to yellow, labeled  "Low T" at the bottom, representing temperature change. The top of the diagram is labeled "Heat" with a black arrow pointing downwards towards a yellow rectangular box labeled “HEAT ENGINE.” From this box, there is a black arrow pointing right to a label “Work.” Below the "Heat Engine" box is a gray arrow pointing downwards towards the bottom of the diagram labeled "(Waste) Heat." The arrows and labels illustrate the flow and conversion of heat energy within the engine.

Credit: © Penn State is licensed under CC BY-NC-SA 4.0

A general expression for the efficiency of a heat engine can be written as:

$$\text{Efficiency =}\frac{\text{Work} }{{\text{Heat Energy} }_{\mathit{\text{Hot}} }}$$

We know that all the energy that is put into the engine has to come out either as work or waste heat. So work is equal to Heat at High temperature minus Heat rejected at Low temperature. Therefore, this expression becomes:

$$\text{Efficiency=}\frac{{\text{Q}}_{\mathit{\text{Hot}}}{\text{-Q}}_{\mathit{\text{Cold}}}}{{\text{Q}}_{\mathit{\text{Hot}}}}$$

Where, Q_Hot = Heat input at high temperature and Q_Cold= Heat rejected at low temperature. The symbol (Greek letter eta) is often used for efficiency this expression can be rewritten as:

$${\eta }^{\prime }\left( \% \right)=1- \frac{Q_{\mathit{\text{Cold}} }}{Q_{\mathit{\text{Hot}} }} \times 100$$

The above equation is multiplied by 100 to express the efficiency as percent.

French Engineer Sadi Carnot showed that the ratio of Q_HighT to Q_LowT must be the same as the ratio of temperatures of high temperature heat and the rejected low temperature heat. So this equation, also called Carnot Efficiency, can be simplified as:

The Carnot Efficiency is the theoretical maximum efficiency one can get when the heat engine is operating between two temperatures:

• The temperature at which the high temperature reservoir operates ( T_Hot ).
• The temperature at which the low temperature reservoir operates ( T_Cold ).

In the case of an automobile, the two temperatures are:

• The temperature of the combustion gases inside the engine ( T_Hot ).
• The temperature at which the gases are exhausted from the engine ( T_Cold ).

Below is a table showing two temperature scales. The scale labeled "HOT," shows the range of temperatures for the combustion of gases in a car engine. The scale labeled "COLD," shows the range of temperatures at which gases are exhausted from the car engine.

Credit: © Penn State is licensed under CC BY-NC-SA 4.0

Instructions: Look carefully at the efficiency numbers in the body of the table. How do the Hot and Cold temperatures' effect on the efficiency.

Answer the following questions based on the information in the Car Engine Efficiency table above.

Let’s look at an example of how temperature differences are used to generate power. Power plants convert chemical energy into electrical power. Here is a video overviewing the operation of a geothermal energy system, a classic thermal power generation plant.

Below are two temperature scales. The scale labeled "HOT," shows the range of temperatures for the combustion of gases in a power plant. The scale, "COLD," shows the range of temperatures at which gases are exhausted from the power plant.

Text description of the Power Plant diagram.

The diagram is labeled "Power Plant." Below the label are two horizontal lines representing temperature scales, labeled "HOT" and "COLD." The "HOT" scale is at the top in dark red, starting at 350°C and marked at 400, 500, 600, 700, 800, 900, and ending at 1000. The "COLD" scale is in blue below, marked at 100°C, 200°C, and 300°C.

Credit: © Penn State is licensed under CC BY-NC-SA 4.0

Look carefully at the efficiency numbers in the body of the table. How do the Hot and Cold temperatures' effect on the efficiency.

Calculating Overall Efficiency

Using the energy efficiency concept, we can calculate the component and overall efficiency:

$$\text{Overall Efficiency}=\frac{\text{Electrical Energy Output}}{\text{Chemical Energy Input}}$$

Here the electrical energy is given in Wh and Chemical Energy in Btus. So Wh can be converted to Btus knowing that there are 3.412 Wh in a Btu.

This overall efficiency can also be expressed in steps as follows:$$\text{Overall Efficiency}=\underset{\text{Efficiency of the Boiler} }{\underbrace{\left[ \frac{\text{Thermal Energy} }{\text{Chemical Energy} }\right] }}\times \underset{\text{Efficiency of the Turbine} }{\underbrace{\left[ \frac{\text{Mechanical Energy} }{\text{Thermal Energy} }\right] }}\times \underset{\text{Efficiency of the Generator} }{\underbrace{\left[ \frac{\text{Electrical Energy} }{\text{Mechanical Energy} }\right] }}$$

$$\text{Overall Efficiency}=\text{Bioler, }\eta \times \text{Turbine, }\eta \times \text{Generator, }\eta$$

Applying this method to the above power plant example:

$$\begin{array}{c}\text{Overall Efficiency}=\left[\frac{88\mathit{\text{Btus}}}{100\mathit{\text{Btus}}}\right]\times \left[\frac{36\mathit{\text{Btus}}}{88\mathit{\text{Btus}}}\right]\times \left[\frac{35\mathit{\text{Btus}}}{36\mathit{\text{Btus}}}\right]\\ \\ =0.88\times 0.41\times 0.97\\ \\ =\mathrm{0.35 }\text{ or }35\%\end{array}$$

It can be seen that the overall efficiency of a system is equal to the product of efficiencies of the individual subsystems or processes. What is the implication of this?

Steps of Overall Efficiency

Previously, we examined the efficiency of individual components, such as an automobile engine or a power plant. However, to understand true energy utilization, we must consider the entire chain of energy transformations. This chain ranges from extracting raw resources to the final use of energy, such as light from a bulb or sound from a stereo.

The process involves five key steps:

1. Production: Mining the coal.
2. Transportation: Moving coal to the power plant.
3. Generation: Converting coal into electricity.
4. Transmission: Sending electricity through power lines.
5. End Use: Converting electricity into light or sound.

Tracking the Energy Flow To calculate the cumulative efficiency, let us trace the energy flow starting with 100 units of energy stored in the ground (measured in BTUs).

• Mining (95% Efficiency): Extracting coal requires energy to operate equipment. For every 100 units in the ground, only 95 units reach the surface.
• Transportation: Trucks consume fuel to move the coal. By the time the coal reaches the power plant, the energy value drops from 95 units to approximately 90 units.
• Electricity Generation (33% Efficiency): Power plants are roughly 33% efficient. When 90 units of coal energy enter the plant, only 30 units emerge as electricity.
• Transmission: High-voltage lines transport electricity to the user. While there are minor losses here, we will estimate that approximately 30 units reach the home.
• End Use (5% Efficiency): Traditional light bulbs are notoriously inefficient, operating at about 5% efficiency. Of the 30 units entering the bulb, only 1.5 units are converted into actual light.

Conclusion We started with 100 units of energy in the ground and ended with 1.5 units of light. Therefore, the overall efficiency is 1.5% (1.5 divided by 100).

This reveals a critical reality: to obtain 1.5 units of useful light, we extract 100 units from natural resources. Along the way, approximately 98.5 units of energy are lost as waste heat or friction during the various conversion processes.

Efficiency of a Light Bulb

If the efficiency of each step is known, we can calculate the overall efficiency of production of light from coal in the ground. The table below illustrates the calculation of overall efficiency of a light bulb.

Efficiency of an Automobile

A similar analysis on automobile efficiency is shown in the Figure below.

Text description of the Overall Automobile Efficiency image.

The image illustrates a flowchart titled "Overall Automobile Efficiency," depicting various stages in the lifecycle of automobile energy usage. The flowchart consists of six main stages, each represented by a distinct black and white icon.

1. Production: An oil rig pumping oil, symbolizing the extraction phase.
2. Transportation: A pipeline with flowing arrows indicates the movement of crude oil.
3. Refining: A factory with smokestacks emits plumes of smoke, representing the refining process.
4. Distribution: A fuel pump is shown, highlighting the distribution stage of refined fuel.
5. Engine: Icons suggest acceleration and deceleration with associated mechanics, detailing the engine's efficiency.
6. Transmission: Diagrams with arrows demonstrate the power transmission process in the automobile.

Each stage is connected with bold black arrows, illustrating the flow of energy from one phase to the next.

Credit: © Penn State is licensed under CC BY-NC-SA 4.0

The table below shows that only about 10% of the energy in the crude oil in the ground is in fact turned into mechanical energy moving people.

In this lesson, you explored one of the most fundamental—and humbling—principles in energy science: no energy conversion is perfect. Every device that transforms energy, from your smartphone to a power plant, loses some portion of its input to waste heat, friction, or other irreversibilities. Here's a synthesis of the core concepts you've mastered:

Heat Engines and the Limits of Efficiency

• Heat engines (like automobile engines, power plants, and even your body) convert thermal energy into mechanical work—but they must reject waste heat to a colder reservoir. This isn't an engineering flaw; it's a consequence of the Second Law of Thermodynamics.
• Carnot efficiency defines the theoretical maximum efficiency for any heat engine operating between two temperatures

$\text{Efficiency} = [1-(Tc/Th) ]*100\%$

Where:

$\text{temperature }\mathit{\text{MUST}}\text{ be in Kelvin}$

• Kelvin is non-negotiable: Because Carnot efficiency depends on a ratio of temperatures, you must use the absolute Kelvin scale (K = °C + 273.15). Using Celsius yields dramatically incorrect (and impossible) results.

  Cascading Efficiency: The Power of Multiplication

• Real-world energy pathways involve multiple sequential steps (e.g., fuel extraction → generation → transmission → end use).
• $\mathbf{\text{Overall efficiency}}\mathbf{=}\mathit{\eta }\mathbf{₁}\mathbf{\times }\mathit{\eta }\mathbf{₂}\mathbf{\times }\mathit{\eta }\mathbf{₃}\mathbf{\times }\mathbf{\text{...}}\mathbf{\times }\mathit{\eta }\mathbf{ₙ}$
• Losses compound: A system with five 90%-efficient steps has an overall efficiency of only 0.9⁵ = 59%. This explains why small improvements at the least efficient step (e.g., replacing incandescent bulbs with LEDs) can yield outsized system-wide gains.

Test Yourself

The questions below are your chance to test and practice your understanding of the content covered in this lesson. In other words, you should be able to answer the following questions if you know the material that was just covered! If you have problems with any of the items, feel free to post your question on the unit message board so your classmates, and/or your instructor, can help you out!

1. A heat engine has Carnot efficiency of 30%. Useful output from the engine is 1,000J. How much heat is wasted?
2. How can we improve the Carnot efficiency of a heat engine by changing the hot and cold reservoir temperatures?
3. Most of the energy conversion devices that we use in our day-to-day life can be classified as Heat Engines. Give two examples.