STIRLING CYCLE WORKING, EFFICIENCY DERIVATION, P-V AND T-S DIAGRAM

Stirling cycle was devised by Stirling. It is a reversible cycle which consists of two isothermal processes and two constant volume processes. The last two processes are performed with the help of a refrigerator to make this cycle reversible. The p-v and t-s diagram of this cycle are shown in the figure.

P-v diagram of Stirling Cycle
T-s diagram of Stirling Cycle

Let us now consider the four stages of the Stirling cycle. Let the engine cylinder contain m kg of air at its original position represented by point 1. At this point, let P1T1, and V1 be the pressure, temperature, and volume of the air respectively.

Stages of an Ideal Stirling Cycle

Following are the four cycles of an Ideal Stirling Cycle:

  1. Isothermal compression (Process 1-2)
  2. Constant volume cooling (Process 2-3)
  3. Isothermal expansion (Process 3-4)
  4. Constant volume heating (Process 4-1)

1. Process 1-2 (Isothermal compression)

The air expands isothermal, practically, at a constant temperature, T1 or T2 from V1 to V2. It means that the temperature T2 (at point 2) is equal to temperature T1. This isothermal expansion is represented by the graph 1-2 in fig. 5-5 (a) and (b). The heat supplied by the external source is absorbed during this process.

Heat supplied = Work done during isothermal expansion

ngcb19
ngcb19
ngcb19
ngcb19

2. Process 2-3 (Constant volume cooling)

The air now passes through the regenerator and is cooled at constant volume to a temperature T3. This process is represented by a graph 2-3 on p-v and T-s diagram. In this process, heat is rejected to the regenerator.

ngcb19
ngcb19

3. Process 3-4 (Isothermal expansion)

The air is now compressed isothermally, practically, at a constant temperature T3 in the engine cylinder from V3 to V4. This process is represented by the graph 3-4 on p-v and T-s diagrams. Again, heat is rejected by the air during this process.

ngcb19
ngcb19
ngcb19
ngcb19
ngcb19

4. Process 4-1 (Constant volume heating)

Lastly, the air is heated at a constant volume to a temperature T1, bypassing it through the regenerator in the reverse direction to that of process 2-3. It may be noted that the air restores initial condition at the end of this process, and completes the cycle. It is thus obvious, that the heat is absorbed by the air from regenerator during this process, i.e., 4-1.

ngcb19

= Heat taken in from the regenerator

ngcb19
ngcb19

We see that the heat rejected to the regenerator during process 2-3 is equal to the heat taken in from the regenerator during the process 4-1. Hence there is no interchange of heat to the system during these processes. The only interchange of heat is during the two isothermal processes.

Work done = Heat supplied – Heat rejected

ngcb19
ngcb19

And efficiency,

ngcb19
ngcb19
ngcb19

Notes:

The efficiency of the Stirling cycle is the same as that of the Carnot cycle. That’s why the cycle is reversible, and all reversible cycles have the same efficiency.

If the efficiency of the regenerator is nr then heat taken in from the regenerator during process 4-1 will be mC0 { T1-T2} (1-nr). In that case,

ngcb19
ngcb19

That’s it.We have studied successfully STIRLING CYCLE WORKING, EFFICIENCY DERIVATION, P-V AND T-S DIAGRAM. Thank you so much for reading in our blog. If you have any questions about the “Stirling cycle” ask in the comments section. If you like this article share with your friends.