The volume of a gas is reduced adiabatically to $\frac{1}{4}$ of its volume at 27°C, if the value of $\gamma = 1.4,$ then the new temperature will be
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For adiabatic change $\mathrm{TV}\gamma^{-1}$ = constant
$\Rightarrow \frac{\mathrm{T}_2}{\mathrm{T}_1} = \left(\frac{\mathrm{V}_1}{\mathrm{V}_2}\right)^{\gamma - 1} \Rightarrow \mathrm{T}_2 = \left(\frac{\mathrm{V}_1}{\mathrm{V}_2}\right)^{\gamma - 1} \times \mathrm{T}_1$ $\Rightarrow \mathrm{T}_2 = \left(\frac{\mathrm{V}}{\mathrm{V}/4}\right)^{1.4 - 1} \times 300 = 300 \times (4)^{0.4} \mathrm{K}$
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