$A$ rigid diatomic gas $(\gamma = 7/5)$ is compressed adiabatically to volume $(V_i/32)$, where $V_i$ is the initial volume. The initial temperature of the gas is $T_i \text{ K}$ and the final temperature is $x T_i \text{ K}$. The value of $x$ is

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_P}{C_V}$ for the gas is

The variation of pressure $P$ with volume $V$ for an ideal monatomic gas during an adiabatic process is shown in the figure. At point $A$,the magnitude of the rate of change of pressure with respect to volume is

$A$ cylinder with a movable piston contains $3$ moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator,and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

$A$ vessel contains $0.15 \ \text{m}^3$ of a gas at pressure $8 \ \text{bar}$ and temperature $140^\circ \text{C}$ with $c_p = 3R$ and $c_v = 2R$. It is expanded adiabatically until the pressure falls to $1 \ \text{bar}$. The work done during this process is . . . . . . $\text{kJ}$.

During an adiabatic process, the pressure of a gas is proportional to the cube of its temperature. The value of $C_p / C_V$ for that gas is