The Second Law of Thermodynamics:Example Uncontrolled Expansion of a Gas.

Example: Uncontrolled Expansion of a Gas

We consider the entropy change for the uncontrolled expansion of an ideal gas in Sec. 3.13, for which the first law gave T1 = T2. The second law for this adiabatic process simply reads

The total change of entropy follows from the ideal gas entropy (with constant specific heat), Eq. (4.19) as

Since in this process the temperature of the ideal gas remains unchanged, the growth of entropy is only attributed to the growth in volume: by filling the larger volume V2, the gas assumes a state of larger entropy. Since the container is adiabatic, there is no flux of entropy over the boundary (i.e., ), Q˙ k = 0), k and all entropy generated stays within the system, Sgen = S2 − S1.

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