Physics Lesson 13.10.5 - Heat Engines

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Welcome to our Physics lesson on Heat Engines, this is the fifth lesson of our suite of physics lessons covering the topic of Entropy and the Second Law of Thermodynamics, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Heat Engines

Heat engines operate by converting heat into mechanical energy, i.e. they produce motion from heat energy. Car motors, diesel engines, steam turbines and steam power plants are all examples of heat engines.

A heat engine uses a gas at high pressure to push against a piston. For this, it needs a source of thermal energy to heat up the gas inside the cylinder. These thermal energy sources originally are in another form, most commonly as chemical energy of fuels. Therefore, the chain of energy conversions in heat engines is

In simple terms, a heat engine absorbs heat energy from a source (called "hot reservoir") at high temperature, then it converts part of this energy into useful work and expels the rest outside the system (in the surroundings). Such a medium is at lower temperature than the system and is known as "cold reservoir" or "heat sink".

A simplified scheme of a heat engine operation is shown in the figure below.

QH represents the amount of heat supplied to the heat engine from a source at high temperature,

QC represents the amount of heat energy given off by the heat engine to a low temperature reservoir, usually the atmosphere,

TH is the absolute temperature of the hot reservoir,

TC is the absolute temperature of the cold reservoir, and

W is the mechanical work done by the heat engine.

The cold reservoir is necessary as otherwise, the heat engine would heat up continuously and eventually, it would melt down. Also, both QH and QC are taken as positive.

For continuous operation, a heat engine must operate in cycles, i.e. it must cool down to the initial temperature before starting the new cycle.

Efficiency of Heat Engines

Efficiency of heat engines is conceptually similar to the efficiency of all mechanical devices, i.e. it represents the ratio of output and input energy of engine. Its formula is

where W is the work done by the engine, which represents the output (or useful) energy and Q is the input (or total) heat energy supplied by the source.

Example 2

400 g of fuel are consumed by a 65 kW heat engine to make a car travel for 4 minutes. The fuel has a calorific value of 45 megajoules/kg. What is the efficiency of the engine? The formula of heat energy released by a burning fuel is

where m is the mass of fuel and q is its calorific value.

Solution 2

Work (or useful energy) is obtained by multiplying power and time. Since 65 kW = 65 000 W and 4 minutes = 240 seconds, we have

The heat energy released by the burning fuel (which represents the total or input energy of the source) is

Therefore, the efficiency of this heat engine is

This means 86.7% of the original heat energy supplied by the source is used to do work while the rest 13.3% is wasted energy that goes into the environment through the cold reservoir during cyclic processes.

Now, we can provide a more formal definition for entropy, which is based on the quantities involved in application of the Second Law of Thermodynamics in thermal engines:

Entropy is a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

You have reached the end of Physics lesson 13.10.5 Heat Engines. There are 6 lessons in this physics tutorial covering Entropy and the Second Law of Thermodynamics, you can access all the lessons from this tutorial below.

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