An ideal gas $(\gamma = 1.5)$ is expanded adiabatically. To reduce the root mean square velocity of molecules two times, the gas should be expanded (in $\times$)

$A$ sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given, $\gamma = 3/2$):

In an adiabatic expansion of a gas, the initial and final temperatures are $T_1$ and $T_2$ respectively. Then, the change in internal energy of the gas is:
$[R = \text{gas constant}, \gamma = \text{adiabatic ratio}]$

$A$ monatomic gas at pressure $P_1$ and volume $V_1$ is compressed adiabatically to $1/8$ of its original volume. What is the final pressure of the gas in terms of $P_1$?

$A$ 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:

$A$ monoatomic ideal gas, initially at temperature $T_{1}$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column before and after the expansion respectively, then the value of $\frac{T_{1}}{T_{2}}$ will be