If $\gamma$ denotes the ratio of two specific heats of a gas, the ratio of the slopes of adiabatic and isothermal $PV$ curves at their point of intersection is:

In a thermodynamic process,there is no exchange of heat between the system and surroundings. Then the thermodynamic process is

$A$ gas for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{4}$ of its initial volume. What is the ratio of the final pressure to the initial pressure?

$A$ 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:

An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules $3$ times (in $\times$)? $(\gamma = 1.5)$

$A$ graph of pressure versus volume for an ideal gas for different processes is as shown. In the graph,curve $OC$ represents: