A cyclic process

In a cyclic process, the system starts and returns to the same thermodynamic state.

The net work involved is the enclosed area on the P-V diagram. If the cycle goes clockwise, the system does work. A cyclic process is the underlying principle for an engine.

If the cycle goes counterclockwise, work is done on the system every cycle. An example of such a system is a refrigerator or air conditioner.

Example of a Cyclic Process

  1. Expansion at constant temperature (T1).
  2. Removal of heat at constant volume (V2).
  3. Compression at constant temperature (T2).
  4. Addition of heat at constant volume (V1).

We'll show that this process does work. Because the process is cyclic, there is no change in internal energy after each cycle. Therefore the net work done in each cycle equals the heat added to the system. We now analyze each of the steps in the cycle.

Step 1 - Isothermal expansion: The system does work W1 which equals the heat Q1 added to the system in the expansion, because the internal energy does not change.

Step 2 - Isochoric process: The work done is W2 = 0. Heat Q2 is removed from the system because the temperature decreases from T1 to T2.

Step 3 - Isothermal compression: The work W3 done by the system is negative, but of smaller magnitude than W1 because the area under the PV curve is less than that in step 1. The internal energy is does not change, so the heat removed is Q3 = W3.

Step 4 - Isochoric process: The reverse of step 2. W4 = 0, while heat Q4 = - Q2 is added to the system.

Cycle Summary

Because W2 and W4 = 0, the net work done is Wnet = W1 + W3

Because Q2 + Q4 =0, the net heat added is Qnet = Q1 + Q3 = Wnet

Net work done:
W1 = nRT1 ln (
V2
V1
)
W3 = nRT2 ln (
V1
V2
)
Wnet = nR (T1 - T2) ln (
V2
V1
)