will AT&T; , 3:36 PM X511.spring2018.midterm.pdf Problem 3 (2x5-10 points) Two c

Question

will AT&T; , 3:36 PM X511.spring2018.midterm.pdf Problem 3 (2x5-10 points) Two containers have identical volumes and numbers of particles but hold different ideal gas species, as depicted in Fig. 1. The containers are then joined and the particles allowed to mix. In one case, they are joined such that the final volume remains the same as each initial container. In another case, they are joined such that the pressure remains the same Write an expression for the change in entropy upon mixing for each case. ES Fig. 1. Two different ideal-gas mixing scenarios. Open with Print

Explanation / Answer

problem 3:

Case 1, Final volume remains

V1 + V2 = V (volume)

N1 + N2 = N (moles)

For entropy:

S = N*k*ln(V/N) + 3/2*N*k

substitute for each case

S1 = N1*k*ln(V1/N1) + 3/2*N1*k

S2 = N2*k*ln(V2/N2) + 3/2*N2*k

Then, add

St = S1+S2 =  N1*k*ln(V1) + 3/2*N1*k+N2*k*ln(V2) + 3/2*N2*k

Common terms:

dS = (N1+N2)k*ln((V1+V2)/(N1+N2)) - N1k*ln(V1/N1) -N2k*ln(V2/N2)

dS = N1*k*ln(V/N*N1/V1) + N2*k*ln(V/N*N2/V2)

nte that V = V1 = V2 and N1 = N2

so

dS = N1*k*ln(1) + N2*k*ln(1)

dS = 0

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