An ideal gas is allowed to undergo a free expansion. If its initial volume is V1 and its final volume is V2, the change in entropy is:
A)nR ln (V2/V1)
B)nRT ln (V2/V1)
C)nk ln (V2/V1)
D)0
E)nR V2/V1

Question

Quizplus · Accepted Answer

During a free expansion, no work is done on or by the system and no heat is transferred. Therefore, change in internal energy is 0 (ΔU = 0). From the first law of thermodynamics, ΔQ = ΔU + ΔW = 0, where ΔW is the work done by the system. As ΔQ = TΔS, this means that ΔS = 0/T = 0, since the temperature cannot be negative. However, this only applies to a reversible process. In an irreversible process, such as free expansion, there is an additional entropy generation due to an increase in disorder of the system, i.e. the particles of the gas spread out over a larger volume. The entropy increase is given by ΔS = nR ln(V2/V1).

An Ideal Gas Is Allowed to Undergo a Free Expansion