ThermodynamicsMedium
Question
Two moles of an ideal gas undergo free expansion from 10 L to 100 L at 300 K . The values of $\Delta S_{\text{system}\text{~}}$ and $\Delta S_{\text{surroundings}\text{~}}$ are
( $R$ is universal gas constant)
Options
A.$\Delta S_{\text{system}\text{~}} = 0;\Delta S_{\text{surroundings}\text{~}} = 4.606R$
B.$\Delta S_{\text{system}\text{~}} = 4.606R;\Delta S_{\text{surroundings}\text{~}} = 0$
C.$\Delta S_{\text{system}\text{~}} = 0;\Delta S_{\text{surroundings}\text{~}} = 0$
D.$\Delta S_{\text{system}\text{~}} = 4.606R;\Delta S_{\text{surroundings}\text{~}} = - 4.606R$
Solution
Sol. [Key Concept: Free expansion of an ideal gas — w = 0, ΔU = 0]
During free expansion
$$\begin{matrix} \Delta S_{\text{system}\text{~}} & \ = nRln\frac{V_{2}}{V_{1}} \\ & \ = 2.303 \times 2 \times R \times log\frac{100}{10} \\ & \ = 4.606R \\ \Delta S_{\text{surroundings}\text{~}} & \ = 0\text{~}\text{as}\text{~}q = 0 \end{matrix}$$
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