Jet aircrafts fly at altitudes above $30000 \,ft$, where the air is very cold at $-40^{\circ} C$ and the pressure is $0.28 \,atm$. The cabin is maintained at $1 \,atm$ pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of $25^{\circ} C$, we will require in addition 

A certain mass of gas at $273 K$ is expanded to $81$ times its volume under adiabatic condition. If $\gamma = 1.25$ for the gas, then its final temperature is ….. $^oC$

A monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be $…..P$

Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$, Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is ………..

One mole of an ideal gas with $\gamma = 1.4$, is adiabatically compressed so that its temperature rises from $27°C$ to $35°C$. The change in the internal energy of the gas is ……. $J$ $(R = 8.3\,J/mol.K)$