Physics Lesson 13.10.6 - Carnot Engine

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Welcome to our Physics lesson on Carnot Engine, this is the sixth 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.

Carnot Engine

The Second Law of Thermodynamics implies that no perfect machine can exist i.e. the efficiency of heat engines cannot be 1. This means there is some heat lost during the process.

The question arisen here is: How to construct a machine with the maximum efficiency possible and what is the value of this maximum efficiency?

From experiments, it is proven that the type of engine that produces the maximum efficiency is the "Carnot Engine", named after the famous French scientist Sadi Carnot. A Carnot engine produces a definite reversible cycle which has a maximum possible efficiency between two given heat reservoirs with different temperatures. In other words, a Carnot cycle is the most efficient cycle that can theoretically exist.

A schematic-graphical representation of a Carnot cycle is shown in the figure below.

From the graph above, you can see that a Carnot cycle consists in two adiabatic and two isothermal processes. All these processes are reversible.

Based on the figure above, we can say that:

• Processes 2-3 and 4-1 are adiabatic. This means no heat is transferred between various parts of the engine.
• Process 1-2 represents an isothermal expansion. During this process, the gas absorbs some heat (QH) from a hot source with temperature TH.
• During the process 3-4, gas is compressed isothermally, giving of some heat (QC) to a cold reservoir with temperature TC.

The figure below shows what happens to the gas produced by the heat source during a Carnot cycle.

For the same difference in temperatures, the Carnot engine is the most efficient among all the other types of engines. However, a Carnot engine is more a theoretical model than a reality. As we have stated earlier, it is quite impossible to obtain reversible cycles during a thermal process. Carnot engine however, is very useful in determining the maximum efficiency a heat engine can have. Hence, we can say the efficiency of a real heat engine operating between the temperatures TH and TC is lower than that of a Carnot engine with the same range of temperatures. Thus, we can write

Two factors decrease the efficiency of a real engine. They are:

1. A real machine does not operate according a Carnot cycle
2. Friction between various parts of the engine decreases further the efficiency

The equation used to find the efficiency in a Carnot engine is

Example 3

A Carnot engine operates between the minimum and maximum temperature of water. What is its efficiency of this engine?

Solution 3

Water exists in liquid state between 0°C and 100°C. The first represents the temperature of cold reservoir (T_C) and the other, that of the hot reservoir (T_H). When converted into Kelvin scale, we obtain T_C = 0 + 273 = 273 K and T_H = 100 + 273 = 373 K.

Therefore, we obtain for the efficiency of this Carnot engine:

This is a small value, which in reality decreases further when we consider the above-mentioned factors. Therefore, most engines operate between higher ranges of temperatures, in order to increase the numerator of fraction, which brings in an increase in the engine's efficiency.

You have reached the end of Physics lesson 13.10.6 Carnot Engine. 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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