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.