An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 = \text{constant}$. The coefficient of volume expansion of the gas is . . . . . . .

Which graph represents the variation of $PV$ with $V$ for a fixed mass of an ideal gas at constant temperature?

The heat energy that must be supplied to $14 \text{ g}$ of nitrogen at room temperature to raise its temperature by $48^{\circ}C$ at constant pressure is ($R$ = gas constant, Molecular weight of nitrogen $(N_2) = 28$) (in $R$)

$A$ fixed mass of gas at constant pressure occupies a volume $V$. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be

$A$ given mass of a gas is allowed to expand freely until its volume becomes double. If $C_b$ and $C_a$ are the velocities of sound in this gas before and after expansion respectively,then $C_a$ is equal to

Read the given statements and decide which is/are correct on the basis of the kinetic theory of gases:
$(I)$ Energy of one molecule at absolute temperature $T = 0 \ K$ is zero.
$(II)$ $r.m.s.$ speeds of different gases are the same at the same temperature.
$(III)$ For one gram of all ideal gases,kinetic energy is the same at the same temperature.
$(IV)$ For one mole of all ideal gases,mean kinetic energy is the same at the same temperature.