An ideal gas is expanded adiabatically at an initial temperature of $300 K$ so that its volume is doubled. The final temperature of the hydrogen gas is $(\gamma = 1.40)$
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(a) $T{V^{\gamma - 1}} = $constant
==> $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^\gamma }$
==> ${T_2} = {T_1}{\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^\gamma }$
$ \Rightarrow {T_2} = 300{\left( {\frac{1}{2}} \right)^{0.4}} = 227.36\;K$
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