The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as

Compressed air in the tube of a bicycle wheel at normal temperature suddenly starts coming out from a puncture. The air inside:

When $2 \text{ moles}$ of a monatomic gas expands adiabatically from a temperature of $80^{\circ} C$ to $50^{\circ} C$,the work done is $W$. The work done when $3 \text{ moles}$ of a diatomic gas expands adiabatically from $50^{\circ} C$ to $20^{\circ} C$ is: (in $W$)

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 $\,K$)

The adiabatic elasticity of a diatomic gas at $NTP$ is ........ $N/m^2$.

In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas $(\gamma = 5/3)$ decreases from $60 \text{ K}$ to $50 \text{ K}$. The work done by the gas in the process is : (Take the universal gas constant as $R = 8.3 \text{ J mol}^{-1} \text{ K}^{-1}$) (in $\text{ J}$)