4.9 Overall 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.