Q33 / 180 · AIIMS 2018 (27 May) · Chemistry

1 mole of an ideal gas expands isothermally reversibly from 2 litre to 4 litre and 3 moles of the same gas expands from 2 litre to $x$ litre and doing same work, what is ' $x$ '?

  • A
    $(8)^{1 / 3}$
  • Correct answer
    B
    $(4)^{2 / 3}$
  • C
    $2$
  • D
    $4$

Solution

$\begin{aligned} & \text { } w=n R T \ln \frac{V_2}{V_1} \\ & R T \ln \frac{4}{2}=3 R T \ln \frac{x}{2} \\ & \ln 2=\ln \left(\frac{x}{2}\right)^3 \\ & x^3=16 \Rightarrow x=(16)^{\frac{1}{3}}=4^{\frac{2}{3}}\end{aligned}$

Hence, the correct answer is option: 'B'.

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