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Q.

Two moles of an ideal monoatomic gas at 27⁰C occupies a volume of V.If the gas is expanded adiabatically to the volume 2V, then the work done by the gas will be $(γ$ 5 /3)

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a

–2767.23J

b

2767.23J

c

2500J

d

–2500J

answer is B.

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Detailed Solution

n = 2moles, $γ = \frac{5}{3}, V_{1} = V; V_{2} = 2 V, T_{1} = 300 K$
$\begin{array}{l} T_{2} = ? \Rightarrow {TV}^{γ - 1} = k \Rightarrow Tα \frac{1}{V^{γ - 1}} \\ T_{2} = {(\frac{V_{1}}{V_{2}})}^{γ - 1} (T_{1}) \Rightarrow T_{2} = {(\frac{V}{2 V})}^{5 / 3 - 1} \\ T_{2} = {(\frac{1}{2})}^{2 / 3} (300); w = \frac{nR}{γ - 1} (T_{1} - T_{2}) \\ \Rightarrow w = \frac{2 \times 8 .314}{5 / 3 - 1} (300 - {(\frac{1}{2})}^{2 / 3} 300) \\ w = 2767 .23 J \end{array}$

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