## 9.47 b

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

ClaireHW
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### 9.47 b

Initially a sample of ideal gas at 323K occupies 1.67L at 4.95 atm. The gas is allowed to expand to 7.33L by two pathways a) isothermal, reversible expansion; b) isothermal irreversible free expansion. Calculate delta S total, delta S, and delta S surroundings for each pathway.

I'm confused on not only how the calculations are preformed, but also what each of these systems would look like.

(Claire Woolson Dis 1K)

Mika Sonnleitner 1A
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### Re: 9.47 b

For irreversible expansion, ΔS is the same as for reversible expansion, because entropy is a state property. So from part (a) calculations, ΔS=+3.84 J/K. To calculate this value, you would use the equation ΔS=nRln (V2/V1).

In free expansion, w=0. This is because in free expansion, the gas expands freely, meaning the volume change of the system is zero. According to the equation w=-PΔV, if ΔV=0, then w=0.

Furthermore, since ΔU=0 in isothermal expansion, and since w=0, q=0 (using the equation ΔU=q+w). This means that no heat is transferred to the surroundings, so ΔSsurroundings=0.

Since ΔStotal=ΔS + ΔSsurroundings, ΔStotal=3.84 J/K + 0 = 3.84 J/K.