1 mole of an ideal gas expands isothermally and reversibly by decreasing pressure form $210 \mathrm{kPa}$ to…

1 mole of an ideal gas expands isothermally and reversibly by decreasing pressure form $210 \mathrm{kPa}$ to $105 \mathrm{kPa}$ at $300 \mathrm{~K}$. What is the work done? $\left(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)$
  1. 1960 J
  2. 864 J
  3. 1296 J
  4. 1729 J

Solution

For Isothermal reversible process, $\begin{aligned} & \mathrm{W}=-2.303 \mathrm{nRT} \log \frac{\mathrm{P}_1}{\mathrm{P}_2} \\ & =-2.303 \times 1 \times 8.314 \times 300 \log \frac{210}{105} \\ & =-2.303 \times 8.314 \times 300 \times \log 2 \\ & =-1729 \mathrm{~J}(\log 2=0.3010) \\ & |\mathrm{W}|=1729 \mathrm{~J} \end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 1)

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