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 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: