When the temperature of an ideal gas is increased by $600 \ K$,the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is .... $^oC$

If a closed container containing gas is in motion and is suddenly stopped,the random motion of the gas molecules will .......

$N$ molecules each of mass $m$ of gas $A$ and $2N$ molecules each of mass $2m$ of gas $B$ are contained in the same vessel at temperature $T$. The mean square of the velocity of molecules of gas $B$ is $v^2$ and the mean square of $x$ component of the velocity of molecules of gas $A$ is $w^2$. The ratio $\frac{w^2}{v^2}$ is

The total internal energy of $2$ moles of a monatomic gas at a temperature $27^{\circ} C$ is $U$. The total internal energy of $3$ moles of a diatomic gas at a temperature $127^{\circ} C$ is:

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement-$1$: The internal energy of a perfect gas is entirely kinetic and depends only on the absolute temperature of the gas and not on its pressure or volume.
Statement-$2$: $A$ perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat,the temperature rise of the gas at constant pressure is lower than that at constant volume.

An ideal gas $(\gamma = 1.5)$ is expanded adiabatically. To reduce the root mean square velocity of the molecules by a factor of $2$,the gas should be expanded by how many times?