Two moles of an ideal monoatomic gas occupy a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ the change in its internal energy.

Consider a thermodynamic process where internal energy $U = A P^2 V$ $(A = \text{constant})$. If the process is performed adiabatically, then:

In adiabatic compression, the decrease in volume is associated with

$A$ 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 expansion respectively,then $T_1/T_2$ is given by

An ideal gas initially at $0^{\circ} C$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamics process is . . . . . . $K.$

$A$ gas undergoes a change in which its pressure $P$ and volume $V$ are related as $PV^{n} = \text{constant}$, where $n$ is a constant. If the specific heat of the gas in this change is zero, then the value of $n$ is $(\gamma = \text{adiabatic ratio})$.