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Two moles of an ideal gas undergo free expansion from 10 L to 100 L at 300 K. The values of $\Delta S_{system}$ and $\Delta S_{surroundings}$ are (R is universal gas constant)
Detailed Solution
Isothermal free expansion of 2 mol: $\Delta S_{sys}=nR\ln\frac{V_2}{V_1}=2R\ln\frac{100}{10}=2R\times2.303=4.606R$. Since $dT=0$, $\Delta U=0$; $P_{ext}=0$, so $W=0$. By the first law, $Q=0$. As no heat is exchanged with the surroundings, $\Delta S_{surr}=-\frac{Q_{sys}}{T}=0$.