Example of the Path Independence of Entropy Change
Consider the following Three Processes, Path A, B, & C between equilibrium states 1 and 2.
Consider the following Three Processes, Path A, B, & C between equilibrium states 1 and 2.
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Path A (Isothermal Expansion): 1 ⇒ 2
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Path C (Constant Volume Heating + Adiabatic Expansion):
Constant Volume Heating: 1 ⇒ 3
Adiabatic Reversible Expansion: 3 ⇒ 2
Total Change:
PATH B (Unrestrained Adiabatic Free Expansion):
The Change in Entropy cannot be calculated along this non-equilibrium path. However, Entropy is a state variable, so that the change in entropy must be equal to the change along any reversible path. Therefore, the Change in Entropy for free expansion must have the same value as we found above for path A or C; namely
