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$2 \mathrm{~moles}$ of the ideal gas at $27^{\circ} \mathrm{C}$ temperature is expanded reversibly from $2 \mathrm{~L}$ to $20 \mathrm{~L}$. Find the entropy change $\left(\mathrm{R}=2 \mathrm{cal} \mathrm{mol}^{-1}\right.$ $\left.\mathrm{K}^{-1}\right)$ :
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The correct answer is:
9.2
$\begin{aligned}
& \Delta \mathrm{S}=2.303 \mathrm{n} \mathrm{R} \log _{10} \frac{\mathrm{V}_2}{\mathrm{~V}_1} \\
& =2.303 \times 2 \times 2 \times \log _{10} \frac{20}{2} \\
& =2.303 \times 2 \times 2 \times 1 \\
& =9.212 \mathrm{cal}
\end{aligned}$
& \Delta \mathrm{S}=2.303 \mathrm{n} \mathrm{R} \log _{10} \frac{\mathrm{V}_2}{\mathrm{~V}_1} \\
& =2.303 \times 2 \times 2 \times \log _{10} \frac{20}{2} \\
& =2.303 \times 2 \times 2 \times 1 \\
& =9.212 \mathrm{cal}
\end{aligned}$
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