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

In the $P-V$ diagram shown,there are two adiabatic parts of the same gas intersecting two isothermals at $T_1$ and $T_2$. The ratio $\left(\frac{V_b}{V_a}\right)$ is equal to

$A$ 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 $K$)

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

$A$ polyatomic gas $\left(\gamma = \frac{4}{3}\right)$ is compressed to $\left(\frac{1}{8}\right)^{\text{th}}$ of its volume adiabatically. If its initial pressure is $p$,its new pressure will be (in $p$)

$A$ diesel engine has a compression ratio of $20:1$. If the initial pressure is $1 \times 10^5 \ Pa$ and the initial volume of the cylinder is $1 \times 10^{-3} \ m^3$, then how much work does the gas do during the compression (in $J$)? (Assume the process as adiabatic) $(C_V=20.8 \ J/mol \ K, \gamma=1.4, (20)^{1.4}=66.3)$