An ideal gas expands adiabatically $(\gamma = 1.5)$. To reduce the root-mean-square (r.m.s.) velocity of the molecules $3$ times, the gas has to be expanded by a factor of: (in $times$)

Two gases of equal mass are in thermal equilibrium. If $P_a, P_b$ and $V_a, V_b$ are their respective pressures and volumes,then which relation is true?

An insulated container contains $4$ moles of an ideal diatomic gas at temperature $T$. Heat $Q$ is supplied to the gas,causing $2$ moles of the gas to dissociate into atoms. If the temperature of the gas remains constant,then:

An ideal gas of molar mass $M$ is contained in a vertical tube of height $H$,closed at both ends. The tube is accelerating vertically upwards with acceleration $g$. Then,the ratio of pressure at the bottom $(P_B)$ and the midpoint $(P_m)$ of the tube will be:

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $3:4$. The ratio of their partial pressures when enclosed in a vessel kept at a constant temperature is $2:3$. The ratio of their densities is

Which one of the following gases possesses the largest internal energy?