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 $[{\rm{Given}}\,\,\gamma \,{\rm{of}}\,{\rm{air}} = \,1.5]$

In an adiabatic process, the density of a diatomic gas becomes $32$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is

Consider a spherical shell of radius $R$ at temperature $T$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume$E=$ $\frac{U}{V} \propto {T^4}$ and pressure $P = \frac{1}{3}\left( {\frac{U}{V}} \right)$ If the shell now undergoes an adiabatic expansion the relation between $T$ and $R$ is

Two samples $A$ and $B$ of a gas initially at the same pressure and temperature are compressed from volume $ V$ to $ V/2$ ($A$ isothermally and adiabatically). The final pressure of $ A$ is

You feel enjoy by having bath in shower in summer but not in winter. Why ?

In the following $P-V$ diagram two adiabatics cut two isothermals at temperatures $T_1$ and $T_2$ (fig.). The value of $\frac{{{V_a}}}{{{V_d}}}$ will be