A sample of a gas in a box is at pressure P₀ and temperature T₀. If the number of molecules is doubled and the total kinetic energy of the gas is kept constant, then the final temperature and pressure will be:

(1) ${\mathrm{T}}_0, {\mathrm{P}}_0$

(2) ${\mathrm{T}}_0, 2{\mathrm{P}}_0$

(3) $\frac{{\mathrm{T}}_0}{2}$, $2{\mathrm{P}}_0$

(4) $\frac{{\mathrm{T}}_0}{2}$, ${\mathrm{P}}_0$

The average velocity of gas molecules is:

(1) proportional to $\sqrt{\mathrm{T}}$.

(2) proportional to T.

(3) zero.

(4) Not possible to determine

Which of the following methods will enable the volume of an ideal gas to be increased four times?

(1) Double the temperature and reduce the pressure to half.

(2) Double the temperature and also double the pressure.

(3) Reduce the temperature to half and double the pressure.

(4) Reduce the temperature to half and reduce the pressure to half.

The average speed of gas molecules is v at pressure P. If by keeping the temperature constant, the pressure of the gas is doubled, then average speed will become:

(1) $\sqrt{2}v$

(2) v

(3) 2v

(4) $\frac{v}{\sqrt{2}}$

Four molecules of a gas have speeds of 1, 2, 3 and 4 km/s. The value of the r.m.s. speed of the gas molecules is:

(1) $\frac{1}{2}\sqrt{15} \mathrm{km}/\mathrm{s}$

(2) $\frac{1}{2}\sqrt{10} \mathrm{km}/\mathrm{s}$

(3) 2.5 km/s

(4) $\sqrt{\frac{15}{2}} \mathrm{km}/\mathrm{s}$

The rms speed of the molecules of an enclosed gas is \(v\). What will be the rms speed if the pressure is doubled, keeping the temperature constant?

The ratio of number of collisions per second at the walls of containers by He and O₂ gas molecules kept at the same volume and temperature is: (assume normal incidence on walls)

(1) 2: 1

(2) 1: 2

(3) $2\sqrt{2}$: 1

(4) 1: $2\sqrt{2}$

An ant is moving on a plane horizontal surface. The number of degrees of freedom of the ant will be:

(1) 1

(2) 2

(3) 3

(4) 6

If a gas has 'f' degree of freedom, the ratio of the specific heats of the gases, $\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{V}}}$ is

(1) $\frac{1+\mathrm{f}}{2}$

(2) $1+\frac{\mathrm{f}}{2}$

(3) $1+\frac{1}{\mathrm{f}}$

(4) $1+\frac{2}{\mathrm{f}}$

Molar specific heat at constant volume, for a non-linear triatomic gas is: (vibration mode neglected)

(1) 3R

(2) 4R

(3) 2R

(4) R