3.2: Efficiency of Energy Conversion Devices

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Efficiency is the useful output of energy and is calculated using

\[ Efficiency = \dfrac{Useful \, Energy \, Output}{Total \, Energy \, Output} \]

Example 1

An electric motor consumes 100 watts (a joule per second (J/s)) of power to obtain 90 watts of mechanical power. Determine its efficiency.

Answer

Input to the electric motor is in the form of electrical energy and the output is mechanical energy.

Using equation 3.2.1,

\[ Efficiency = \dfrac{Mechanical \, Power}{Electrical \, Power} = \dfrac{90 \, W}{100 \, W} = 0.9 \nonumber\]

Therefore, the efficiency is 90%.

Caution: if the two variables were measured differently, you would need to convert them to equivalent forms before performing the calculation.

For extra practice similar to Example 1, use this link to generate random practice problems.

Example 2

The United States' power plants consumed 39.5 quadrillion Btus of energy and produced 3.675 trillion kWh of electricity. What is the average efficiency of the power plants in the U.S.?

Answer

Assume that the total energy input equals the total energy output.

\[ Total \, Energy \, Input = 39.5 * 10^15 \, BTUs \nonumber\]

\[ Useful \, Energy \, Output = 3.675 * 10^12 \, kWh \nonumber\]

We are given that 1 kWh = 3412 BTUs. Therefore, to convert all units to BTUs,

\[ Useful \, Energy \, Output = 3.675 * 10^12 \, kWh * \dfrac{3412 \, BTUs}{kWh} = 1.254 * 10^16 \, BTUs \nonumber\]

Then, use equation 3.2.1 to obtain

\[ Efficiency = \dfrac{1.254 * 10^16 \, BTUs}{39.5 * 10^15 \, BTUs} = 0.3174

Therefore, the power plants have an average efficiency of 31.74%.

For extra practice similar to Example 2, use this link to generate random practice problems.

Energy Efficiencies

Energy efficiencies are not 100% and sometimes they are pretty low. Table 3.2.1 shows typical efficiencies of some of the devices that are used in everyday life.

Table 3.2.1. Typical efficiencies of day to day devices

Device	Efficiency
Electric motor	90%
Home gas furnace	95%
Home oil furnace	80%
Home coal stove	75%
Steam boiler in a power plant	90%
Overall power plant	36%
Automobile engine	25%
Electric bulb (incandescent)	5%
Electric bulb (fluorescent)	20%

From our discussion on national and global energy usage patterns in Chapter 2, we have seen that

About 40% of the US energy is used in power generation
About 27% 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?

It turns out that there are some natural limitations when converting energy from heat to work.