The $rms$ speed of a molecule of a diatomic gas is $v$. When the temperature is doubled,the molecule dissociates into two atoms. The new $rms$ speed of the atom is:

The density of hydrogen gas at standard atmospheric pressure $(P = 1.01 \times 10^{5} \ Pa)$ is $0.09 \ kg/m^{3}$. Find the root mean square velocity $(v_{rms})$ and the average kinetic energy of $1 \ mole$ of the gas.

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic),the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement among the following is:

The temperature of an ideal gas is increased from $120 \ K$ to $480 \ K.$ If at $120 \ K,$ the root mean square velocity of the gas molecules is $v,$ at $480 \ K$ it becomes

The curve between absolute temperature $T$ and ${v^2}_{rms}$ is

$A$ certain amount of an ideal gas is taken from its initial state $1$ to final state $4$ through the path $1 \rightarrow 2 \rightarrow 3 \rightarrow 4$ as shown in the figure. $AB, CD, EF$ are all isotherms. If $v_p$ is the most probable speed of the molecules, then: