Match Column-I and Column-II and choose the correct match from the given choices.

Column-I (P) Root mean square speed of gas molecules (Q) The pressure exerted by an ideal gas (R) The average kinetic energy of a molecule (S) The total internal energy of a mole of a diatomic gas

Column-II (1) $\frac{1}{3}nm\bar{v}^2$ (2) $\sqrt{\frac{3RT}{M}}$ (3) $\frac{5}{2}RT$ (4) $\frac{3}{2}k_BT$

The mean free path l for a gas molecule depends upon the diameter, d of the molecule as:

The value $\gamma = \frac{C_P}{C_V}$ for hydrogen, helium, and another ideal diatomic gas $X$ (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:

An ideal gas at $0^\circ\text{C}$ and atmospheric pressure $P$ has volume $V$. The percentage increase in its temperature needed to expand it to $3V$ at constant pressure is:

The root-mean-square speed of hydrogen molecules at 300 K is 1930 m/s. Then the root mean square speed of oxygen molecules at 900 K will be:

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_P$ and $C_V$ respectively. If $\gamma = C_P/C_V$ and $R$ is the universal gas constant, then $C_V$ is equal to:

In the given V-T diagram, what is the relation between pressure $P_1$ and $P_2$?

One mole of an ideal monatomic gas undergoes a process described by the equation $PV^3 = \text{constant}$. The heat capacity of the gas during this process is:

The volume occupied by the molecules contained in $4.5 \text{ kg}$ water at STP, if the molecular forces vanish away, is: