An ideal gas at a pressures of $1$ atmosphere and temperature of ${27^o}C$ is compressed adiabatically until its pressure becomes $8$ times the initial pressure, then the final temperature is ….. $^oC$ ($\gamma  = 3/2$)

Air is filled in a motor tube at ${27^o}C$ and at a pressure of $8$ atmospheres. The tube suddenly bursts, then temperature of air is $[{\rm{Given}}\,\,\gamma \,{\rm{of}}\,{\rm{air}} = \,1.5]$

An ideal monoatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2\, V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2\,V$, the final pressure is $P_a$ . The ratio $\frac{{{P_a}}}{{{P_i}}}$ is

A certain amount of gas is taken through a cyclic process $(A\,B\,C\,D\,A)$  that has two isobars, one isochore and one isothermal. The cycle can be represented on a $P-V$ indicator diagram as

One mole of an ideal gas at an initial temperature of $T\, K$ does $6\, R\, joules$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $\frac{5}{3}$ , the final temperature of gas will be