Given ΔS, find V2

Problem

One mole of an ideal gas at $T=400\;\text{K}$ expands isothermally. It is measured that $\Delta S=11{,}5\;\text{J/K}$. Find the final volume ratio $V_2/V_1$.

Solution

For an isothermal expansion of an ideal gas $\Delta S=nR\ln\frac{V_2}{V_1}$. Inverting with $n=1$ and $R=8{,}31\;\text{J/(mol·K)}$: $\ln\frac{V_2}{V_1}=\frac{\Delta S}{nR}=\frac{11{,}5}{8{,}31}=1{,}384$ Hence: $\frac{V_2}{V_1}=e^{1{,}384}=4{,}0$ $\ev{V_2/V_1\approx 4{,}0}$

Links

Topics: Entropy and the second law Concepts: Entropy · Thermodynamic processes Skills: Entropy balance Objects: Ideal gas