A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_1$ (in Kelvin) and the final temperature is $a T_1$, the value of $a$ is
IIT 2010, Diffcult
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$ \mathrm{TV}^{\gamma-1}=\text { constant } $
$ \mathrm{TV}^{7 / 5-1}=\mathrm{aT}\left(\frac{\mathrm{v}}{32}\right)^{7 / 5-1} $
$ \therefore \mathrm{a}=4 .$
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