Air enters an adiabatic compressor at 300 K. The exit temperature for a compression ratio of 3, assuming air to be an ideal gas $$\left( {\gamma = \frac{{{{\text{C}}_{\text{p}}}}}{{{{\text{C}}_{\text{v}}}}} = \frac{7}{5}} \right)$$   and the process to be reversible, is

Solution (By Examveda Team)

We know for an ideal gas at adiabatic conditions
\[\begin{array}{l} T{V^{\gamma - 1}} = {\rm{CONSTANT}}\\ \Rightarrow T{\left( {\frac{{RT}}{P}} \right)^{\gamma - 1}} = {\rm{CONSTANT}}\\ \Rightarrow T{P^{\frac{{1 - \gamma }}{\gamma }}} = {\rm{CONSTANT}}\\ {\rm{So, }}\,\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{{\gamma - 1}}{\gamma }}} \end{array}\]
$$ \Rightarrow $$  given compression ratio $$\frac{{{P_2}}}{{{P_1}}} = 3{\text{ and }}\gamma = \frac{7}{5}$$
$${\text{So, }}{T_2} = 300{\left( 3 \right)^{\frac{2}{7}}}.$$