At ${27^o}C$ a gas is suddenly compressed such that its pressure becomes $\frac{1}{8}th$ of original pressure. Temperature of the gas will be $(\gamma = 5/3)$
Medium
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(d) ${T^\gamma }{P^{1 - \gamma }} = $constant ==> $T \propto {P^{\frac{{\gamma - 1}}{\gamma }}}$
==> $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{{\gamma - 1}}{\gamma }}} = {\left( {\frac{1}{8}} \right)^{\frac{{5/3 - 1}}{{5/3}}}}$
${T_2} = 300 \times {\left( {\frac{1}{8}} \right)^{0.4}} = 131K = - 142^\circ C$
==> $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{{\gamma - 1}}{\gamma }}} = {\left( {\frac{1}{8}} \right)^{\frac{{5/3 - 1}}{{5/3}}}}$
${T_2} = 300 \times {\left( {\frac{1}{8}} \right)^{0.4}} = 131K = - 142^\circ C$
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