If one litre of an ideal gas at a pressure of $20 \mathrm{~atm}$ expands isothermally and reversibly to a…

If one litre of an ideal gas at a pressure of $20 \mathrm{~atm}$ expands isothermally and reversibly to a final volume of ' $\mathrm{X}$ ' $\mathrm{L}$ by absorbing 92.12 L. atm heat, ' $\mathrm{X}$ ' (in L) is
  1. 200
  2. 20
  3. 15
  4. 100

Solution

$\begin{aligned} & \text { } \mathrm{W}_{\mathrm{rev}}=-2.303 \mathrm{RT} \log \frac{\mathrm{V}_2}{\mathrm{~V}_1} \\ & =-2.303 \mathrm{P}_1 \mathrm{~V}_1 \log \frac{\mathrm{V}_2}{\mathrm{~V}_1} \\ & =-2.303(20)(1.0) \log -=-46.06 \log \frac{\mathrm{V}_2}{1} \\ & =-46.06 \log \mathrm{V}_2 \\ & =-92.12 \mathrm{~L} \text { atm } \Rightarrow \log \mathrm{V}_2=2 \Rightarrow \mathrm{V}_2=100 \mathrm{~L}\end{aligned}$

Asked in: AP EAMCET 2023 (18 May Shift 2)

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