## 9.35

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

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Joined: Fri Sep 28, 2018 12:27 am

### 9.35

Why does A, the monatomic gas have a larger enthalpy change than a diatomic gas?

Kristen Kim 2K
Posts: 70
Joined: Fri Sep 28, 2018 12:16 am

### Re: 9.35

Container A has a greater number of particles than the other containers. Therefore, the entropy change is greater. In comparing monatomic with diatomic, there will be more of the monatomic particles because it needs twice as many particles to equal one diatomic particle.

Aili Ye 4L
Posts: 58
Joined: Fri Sep 28, 2018 12:16 am

### Re: 9.35

Here's a more detailed explanation taken from Lavelle's Chem 14B Solution Manual Errors 6th Edition pdf:
"Students are asked to rank the delta S for a series of gases during a temperature change.
∆S = nCv ln(T2/T1) for an isochoric process Gas A (1.00 mol monatomic ideal):
∆S = nCv ln(T2/T1) = (1.00 moles)(3R/2)ln(T2/T1) and because all undergo the same temperature change, delta S is essentially 3R/2.
Gas B (0.5 mol diatomic, no vibrational degrees of freedom):
∆S = nCv ln(T2/T1) = (0.5 moles)(5R/2)ln(T2/T1) and because all undergo the same
temperature change, delta S is essentially 5R/4.
Gas C (0.5 mol diatomic, 1 vibrational degree of freedom):
∆S = nCv ln(T2/T1) = (0.5 moles)(3R)ln(T2/T1) and because all undergo the same
temperature change, delta S is essentially 3R/2.
The answer provided (B < C < A) is incorrect. The answer should be B < (C = A)."

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