Stirling cycle is a thermodynamic cycle upon which a Stirling Engine works. Stirling engine is a closed cycle regenerative heat engine. It works on either air or any other gas.
Stirling cycle is invented by Robert Stirling with help from his brother (in 1816).
Below are P-V and T-S Diagrams of the Stirling Cycle.
Stirling Cycle is comprised of four processes
Process 1-2
It is isothermal heat addition process. Volume of the system increases due to isothermal heat addition. A little drop in pressure also happens in this process.
Process 2-3
It is isochoric heat removal process. Both temperature and pressure of the system decreases due to isochoric heat removal.
Process 3-4
It is isothermal heat removal process. It is a compression process hence pressure of the system increases and volume decreases.
Process 4-1
It is isochoric heat addition process. Both temperature and pressure of the system increases due to isochoric heat addition.
Below is the table which shows heat and work interactions of the Stirling cycle, along with the change in the internal energy.
| Process | Change in Internal Energy | Heat Interaction | Work Interaction |
| Process 1-2 | 0 | RT1 ln(V2/V1) | RT1 ln(V2/V1) |
| Process 2-3 | CV(T3-T2) | CV(T3-T2) | 0 |
| Process 3-4 | 0 | RT3 ln(V4/V3) | RT3 ln(V4/V3) |
| Process 4-1 | CV(T1-T4) | CV(T1-T4) | 0 |
Note: Negative value of heat interaction indicates heat rejected by the system and positive value of heat interaction indicates heat added to the system. Positive value of work interaction indicates work done by the system and negative value of work interaction indicates work done on the system.
Efficiency of Stirling Cycle
Efficiency of the Stirling Cycle is the ratio of work output to the heat input.
Work output = [RT1 ln(V2/V1) + CV(T1-T4)] – [CV(T2-T3) + RT3 ln(V3/V4)]
Heat Input = RT1 ln(V2/V1) + CV(T1-T4)
Efficiency = Work Output/Heat Input
After putting values of heat input and work output in the above formula, we get
η = 1 – [(CV(T2-T3) + RT3 ln(V3/V4))/(RT1 ln(V2/V1) + CV(T1-T4))] … (1)
Since, Stirling cycle is a regenerative cycle hence heat rejected in process 2-3 is used for heat addition in process 4-1.
It means CV(T2-T3) gets cancelled by CV(T1-T4) hence, we can replace these values by zero in equation (1).
Also, V3/V4 = V2/V1
Hence, new thermal efficiency (after solving equation (1))
η = 1 – (T3/T1)
Which is equal to Carnot Cycle efficiency.
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