If the radius of an $O_{2}$ molecule is $40 \; \mathring{A}$,$T = 27^{\circ}C$,and $P = 1 \; \text{atm}$,find the relaxation time.

In the adjoining figure,various isothermals are shown for a real gas. Then

The internal energy of real gases is determined by which of the following?

There are two identical chambers,completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers into two compartments. Compartment $1$ is filled with an ideal gas and Compartment $3$ is filled with a real gas. Compartments $2$ and $4$ are vacuum. $A$ small hole (orifice) is made in the partition walls and the gases are allowed to expand into the vacuum.
Statement $-1$: No change in the temperature of the gas takes place when an ideal gas expands in a vacuum. However,the temperature of a real gas goes down (cooling) when it expands in a vacuum.
Statement $-2$: The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential.

The value of critical temperature in terms of van der Waals' constants $a$ and $b$ is given by

An ideal gas is enclosed in a cylinder at a pressure of $2 \, atm$ and a temperature of $300 \, K$. The mean time between two successive collisions is $6 \times 10^{-8} \, s$. If the pressure is doubled and the temperature is increased to $500 \, K$,the mean time between two successive collisions will be close to: