The pressure and density of a diatomic gas $(\gamma = 7/5)$ change adiabatically from $(P, d)$ to $(P', d')$. If $\frac{{d'}}{d} = 32$, then $\frac{{P'}}{P}$ should be

The slopes of isothermal and adiabatic curves are related as

The pressure and volume of an ideal gas are related as $\mathrm{PV}^{3 / 2}=\mathrm{K}$ (Constant). The work done when the gas is taken from state $A\left(P_1, V_1, T_1\right)$ to state $\mathrm{B}\left(\mathrm{P}_2, \mathrm{~V}_2, \mathrm{~T}_2\right)$ is :

An engine takes in $5$ moles of air at $20\,^{\circ} C$ and $1$ $atm,$ and compresses it adiabaticaly to $1 / 10^{\text {th }}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be $X\, kJ$. The value of $X$ to the nearest integer is

Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$, Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is ...........

The adiabatic elasticity of hydrogen gas $(\gamma = 1.4)$ at $NTP$ is