A given ideal gas with $\gamma = \frac{{{C_p}}}{{{C_v}}} = 1.5$ at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be ..... $T$
AIEEE 2012, Medium
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$T V^{\gamma-1}=\text { constant }$
$T_{1} V_{1}^{\gamma-1}=\mathrm{T}_{2} V_{2}^{\gamma-1}$
$\Rightarrow T(V)^{1 / 2}=\mathrm{T}_{2}\left(\frac{V}{4}\right)^{1 / 2}$
$\left[\because \gamma=1.5, T_{1}=T, V_{1}=V \text { and } V_{2}=\frac{V}{4}\right]$
$\therefore \quad T_{2}=\left(\frac{4 V}{V}\right)^{1 / 2} T=2 T$
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