An ideal gas undergoes an adiabatic process obeying the relation $PV^{4/3} = \text{constant}$. If its initial temperature is $300 \ K$ and its pressure is increased up to four times its initial value, then the final temperature is (in Kelvin):

In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) is:

$A$ cylinder with a movable piston contains $3$ moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator,and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

For an adiabatic process,if $\gamma = 2.5$ and the volume becomes $1/8$ of its initial volume,then the new pressure $P'$ is (initial pressure $= P$):

$A$ 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 $P_1$?

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 . . . . . . $J$.