$A$ gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$

$A$ certain volume of a gas at $300 \ K$ expands adiabatically until its volume is doubled. The resultant fall in temperature of the gas is nearly (The ratio of the specific heats of the gas $\gamma = 1.5$) (in $K$)

One mole of nitrogen gas being initially at a temperature of $T_0 = 300 \,K$ is adiabatically compressed to increase its pressure $10$ times. The final gas temperature after compression is (Assume, nitrogen gas molecules as rigid diatomic and $100^{1/7} = 1.9$) (in $\,K$)

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in the $P-V$ diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

Two moles of an ideal monoatomic gas occupy a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ the change in its internal energy.

In summer,when the valve of a bicycle tube is removed,the escaping air appears cold. Why?