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In a cyclic process, the system starts in a particular state and returns to that state after undergoing a few different processes. The net work involved is the enclosed area on the P-V diagram.
If the cycle goes clockwise, the system does work. This is the case for an engine.
If the cycle goes counter-clockwise, work is done on the system every cycle. An example of such a system is a refrigerator or air conditioner.
Let's say our sample process consists of the following four steps:
We'll show that the system does work in this process. Because the system returns to its initial state there is no change in internal energy after going once around the cycle. The net work done in each cycle must equal the heat added to the system during the cycle.
Let's analyze each of the steps in the cycle.
Step 1 - Isothermal expansion
The system does work W1 which must be equal to the heat Q1 added to the system in the expansion, because the internal energy does not change.
Step 2 - Isochoric process
The work done in this step is W2 = 0. An amount of heat Q2 is removed from the system because the internal energy decreases (the temperature changes from T1 to T2).
Step 3 - Isothermal compression
The work W3 done by the system is negative, but of smaller magnitude than W1. The area under the PV curve is clearly less than that involved in step 1. The internal energy is does not change, so Q3 = W3 (heat is removed).
Step 4 - Isochoric process
The opposite of step 2. W4 = 0, and the change in internal energy is the same size, just positive instead of negative, as in step 2 so Q2 = -Q4.
Cycle Summary
Because W2 and W4 = 0, the net work done is Wnet = W1 + W3
Because Q2 cancels Q4, the net heat added is Qnet = Q1 + Q3 = Wnet
We can take this further and state the net work in terms of T1, T2, V1, and V2.
| W1 | = nRT1 ln | ( |
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| W3 | = nRT2 ln | ( |
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| Wnet | = nR (T1 - T2) ln | ( |
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