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One mole of an ideal gas expanded isothermally and reversibly 2L to 4L. If 3 moles of this gas (doing same work) expands 2L to x L, then the value of 'x' will be

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$8^{(\frac{1}{3})}$

${(4)}^{\frac{2}{3}}$

answer is B.

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Detailed Solution

W = - nRT $\ln \frac{V_{2}}{V_{1}}$

-RTln $\frac{4}{2}$ = -3RTln $\frac{X}{2}$

ln2 =ln ${(\frac{X}{2})}^{3}$ ; X³ = 16

X = ${(16)}^{\frac{1}{3}}$

x = ${(4)}^{\frac{2}{3}}$

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