Speed of sound in a gas is $v$ and $r.m.s.$ velocity of the gas molecules is $c.$ The ratio of $v$ to $c$ is

One kg of a diatomic gas is at a pressure of $8 \times 10^4 \; N/m^2$. The density of the gas is $4 \; kg/m^3$. What is the energy (in $\times 10^4 \; J$) of the gas due to its thermal motion?

The average translational kinetic energy of ${N}_{2}$ gas molecules at $... {}^{\circ} {C}$ becomes equal to the ${K.E.}$ of an electron accelerated from rest through a potential difference of $0.1 \ V$. (Given ${k}_{B} = 1.38 \times 10^{-23} \ J/K$). (Fill the nearest integer).

An insulated box containing a diatomic gas of molar mass $M$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-

$A$ vessel of volume $V$ contains an ideal gas having mass density $\rho$ at temperature $T$ and pressure $p$. After a portion of the gas is let out, the pressure in the vessel is decreased by $\Delta p$. The mass of the released gas is

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