$A$ 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 $p$)

$A$ cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) compartments at the same $P, V, T$. Heating is started from the left side until the pressure changes to $\frac{27P}{8}$. If the initial volume of each compartment was $9 \text{ litres}$, then the final volume in the right-hand side compartment is . . . . . . litres. (for this ideal gas $\gamma = C_P/C_V = 1.5$)

Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$,where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$ in Kelvin. The value of $x$ is:

During a thermodynamic process, the increase in internal energy of a system is equal to the work done on the system. Which process does the system undergo?

$A$ gas is suddenly compressed such that its absolute temperature is doubled. If the ratio of the specific heat capacities of the gas is $1.5$, then the percentage decrease in the volume of the gas is