# Carnot Cycle

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

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.