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

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

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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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