What is the work done when 2 mole of an ideal gas are expanded isothermally and reversibly from $5…

What is the work done when 2 mole of an ideal gas are expanded isothermally and reversibly from $5 \mathrm{~m}^{3}$ to $10 \mathrm{~m}^{3}$ at $300 \mathrm{~K} ?\left(\mathrm{R}=8 \cdot 314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$
  1. $-34.58 \mathrm{~kJ}$
  2. $3 .458 \mathrm{~kJ}$
  3. $-1.728 \mathrm{~kJ}$
  4. $-3 \cdot 458 \mathrm{k}$

Solution

$\mathrm{n}=2$ mole, $\quad V_{1}=5 \mathrm{~m}^{3}, V_{2}=10 \mathrm{~m}^{3}$ $\mathrm{T}=300 \mathrm{~K}, \quad \mathrm{R}=8.314 \mathrm{~JK}^{-1} \mathrm{~mol}^{-1}$ $\mathrm{W}_{\max }=-2.303 \mathrm{nRT} \log _{10} \frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}$ $\therefore W_{\max }=-2.303 \times 2 \times 8.314 \times 300 \log _{10} \frac{10}{5}$ $=-3457.97 \mathrm{~J}$ $\therefore \mathrm{W}_{\max }=-3.458 \mathrm{~kJ}$

Asked in: MHT CET 2020 (20 Oct Shift 1)

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