A gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$
Medium
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(a) $\because \;T{V^{\gamma - 1}} = $constant $⇒$ ${T_1}V_1^{\gamma - 1} = {T_2}V_2^{\gamma - 1}$
$⇒$ ${T_2} = {T_1}{\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{\gamma - 1}} = {T_1}{(4)^{1.5 - 1}} = 2{T_1}$
change in temperature
$ = {T_2} - {T_1} = 2{T_1} - {T_1} = {T_1} = 273\,K$
$⇒$ ${T_2} = {T_1}{\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{\gamma - 1}} = {T_1}{(4)^{1.5 - 1}} = 2{T_1}$
change in temperature
$ = {T_2} - {T_1} = 2{T_1} - {T_1} = {T_1} = 273\,K$
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