Carnot Cycle was devised by Nicolas Leonard Sadi Carnot, to analyse the problem of the efficiency of a heat engine. In a Carnot cycle, the working substance is subjected to a cyclic operation consisting of two isothermal and two reversible adiabatic or isentropic operations. The p—v and T — s diagram of this cycle is shown in Fig. 5.7 (a) and (b) respectively. Let the engine cylinder contain m kg of air at its original condition as represented by point 1. It may be noted that
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)
1. During isothermal expansion, as shown by 1-2 in Fig. 5.7 the heat supplied is fully absorbed by the-air and is utilized in doing external work.
Heat supplied = Workdone by the air during isothermal expansion
![](data:image/png;base64,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)
2. During reversible adiabatic or isentropic expansion, as shown by 2-3 in Fig. 5.7, no heat is absorbed or rejected by the air.
Decrease in internal energy = Workdone by the air during adiabatic expansion
![](data:image/png;base64,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)
3. During isothermal compression, as shown by 3 – 4 in Fig. 5.7, the heat is rejected and is equal to the workdone on the air.
Heat rejected = Workdone on the air during isothermal compression
![](data:image/png;base64,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)
Note: The expansion and compression ratio (r) must be equal, otherwise the cycle would not close.
4. During reversible adiabatic or isentropic compression, as shown by 4 –1 in Fig 5.7, no heat is absorbed or rejected by the air.
Increase in internal energy = Workdone on the air during adiabatic compression
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)
We see from the above discussion that the decrease in internal energy during reversible adiabatic expansion 2-3 is equal to the increase in internal energy during reversible adiabatic compression 4 -1. Hence their net effect during the whole cycle is zero. We know that
Work done = Heat supplied — Heat rejected
![](data:image/png;base64,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)
Notes:
1. From the above equation, we see that the efficiency of Carnot's cycle increases as T1 is increased or T2 is decreased. In other words, the heat should be taken in at as high a temperature as possible, and rejected at as low a temperature as possible. It may be noted that 100% efficiency can be achieved, only, if T2 reaches absolute zero, though it is impossible to achieve in practice.
2. It may be noted that it is impossible to make an engine working on Carnot's cycle. The simple reason for the same is that the isothermal expansion 1 - 2 will have to be carried out extremely slow to ensure that the air is always at temperature T1. Similarly, the isothermal compression 3 - 4 will have to be carried out extremely slow. But reversible adiabatic expansion 2-3 and reversible adiabatic compression 4 - 1 should be carried out as quickly as possible, in order to approach ideal adiabatic conditions. We know that sudden changes in the speed of an engine are not possible in actual practice. Moreover, it is impossible to completely eliminate friction between the various moving parts of the engine, and also heat losses due to conduction, radiation, etc. It is thus obvious, that it is impossible to realise Carnot's engine in actual practice. However, such an imaginary engine is used as the ultimate standard of comparison of all heat engines.
1. During isothermal expansion, as shown by 1-2 in Fig. 5.7 the heat supplied is fully absorbed by the-air and is utilized in doing external work.
Heat supplied = Workdone by the air during isothermal expansion
2. During reversible adiabatic or isentropic expansion, as shown by 2-3 in Fig. 5.7, no heat is absorbed or rejected by the air.
Decrease in internal energy = Workdone by the air during adiabatic expansion
3. During isothermal compression, as shown by 3 – 4 in Fig. 5.7, the heat is rejected and is equal to the workdone on the air.
Heat rejected = Workdone on the air during isothermal compression
Note: The expansion and compression ratio (r) must be equal, otherwise the cycle would not close.
4. During reversible adiabatic or isentropic compression, as shown by 4 –1 in Fig 5.7, no heat is absorbed or rejected by the air.
Increase in internal energy = Workdone on the air during adiabatic compression
We see from the above discussion that the decrease in internal energy during reversible adiabatic expansion 2-3 is equal to the increase in internal energy during reversible adiabatic compression 4 -1. Hence their net effect during the whole cycle is zero. We know that
Work done = Heat supplied — Heat rejected
Notes:
1. From the above equation, we see that the efficiency of Carnot's cycle increases as T1 is increased or T2 is decreased. In other words, the heat should be taken in at as high a temperature as possible, and rejected at as low a temperature as possible. It may be noted that 100% efficiency can be achieved, only, if T2 reaches absolute zero, though it is impossible to achieve in practice.
2. It may be noted that it is impossible to make an engine working on Carnot's cycle. The simple reason for the same is that the isothermal expansion 1 - 2 will have to be carried out extremely slow to ensure that the air is always at temperature T1. Similarly, the isothermal compression 3 - 4 will have to be carried out extremely slow. But reversible adiabatic expansion 2-3 and reversible adiabatic compression 4 - 1 should be carried out as quickly as possible, in order to approach ideal adiabatic conditions. We know that sudden changes in the speed of an engine are not possible in actual practice. Moreover, it is impossible to completely eliminate friction between the various moving parts of the engine, and also heat losses due to conduction, radiation, etc. It is thus obvious, that it is impossible to realise Carnot's engine in actual practice. However, such an imaginary engine is used as the ultimate standard of comparison of all heat engines.
Great work.
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