In an adiabatic change,the pressure $P$ and temperature $T$ of a monoatomic gas are related by the relation $P \propto T^C$,where $C$ equals

The volume of a gas is reduced adiabatically to $\frac{1}{4}$ of its initial volume at $27^{\circ}C$. If the value of $\gamma = 1.4$,then the new temperature will be:

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V_{final} = 27V$ is . . . . . . $J$.

$A$ given system undergoes a change in which the work done by the system equals the decrease in its internal energy. The system must have undergone an

$A$ 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:

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: