A monoatomic gas $\left( {\gamma  = \frac{5}{3}} \right)$ is suddenly compressed to $\frac{1}{8}$ of its original volume, then the pressure of gas will change to how many times the initial pressure?

If $\gamma = 2.5$ and volume is equal to $\frac{1}{8}$ times to the initial volume then pressure $P' $ is equal to (Initial pressure $= P$)

$Assertion :$ In adiabatic compression, the internal energy and temperature of the system get decreased.
$Reason :$ The adiabatic compression is a slow process.

$5.6$ $liter$ of helium gas at $STP$ is adiabatically compressed to $0.7$ $liter$. Taking the initial temperature to be $T_1$, the work done in the process is

If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?

A monatornic gas at a pressure $P,$ having a volume $V$ expands isothermally to a volume $2\, V$ and then adiabatically to a volume $16\, V.$ The final pressure of the gas is $(\,Take \,\gamma = 5/3)$