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

A mixture of ideal gases has 2 moles of He, 4 moles of oxygen and 1 mole of ozone at absolute temperature T. The internal energy of the mixture is:

(1) 13RT

(2) 11RT

(3) 16RT

(4) 14RT

E₀ and E_H respectively represent the average kinetic energy of a molecule of oxygen and hydrogen. If the two gases are at the same temperature, which of the following statement is true?

(1) E₀  > E_H

(2) E₀  = E_H

(3) E₀  < E_H

(4) Data insufficient

14 g of CO at 27 ^oC is mixed with 16 g of O₂ at 47 ^oC. The temperature of the mixture is: (vibration mode neglected)

(1) - 5 ^oC

(2) 32 ^oC

(3) 37 ^oC

(4) 27 ^oC

When one mole of a monatomic gas is mixed with one mole of a diatomic gas, then the equivalent value of $\gamma$ for the mixture will be: (vibration mode neglected)

(1) 1.33

(2) 1.40

(3) 1.50

(4) 1.6

A box of negligible mass containing 2 moles of an ideal gas of molar mass M and adiabatic exponent $\gamma$ moves with constant speed v on a smooth horizontal surface. If the box suddenly stops, then the change in the temperature of the gas will be:

(1) $\frac{(\mathrm{\gamma }-1){\mathrm{Mv}}^2}{4\mathrm{R}}$

(2) $\frac{{\mathrm{\gamma Mv}}^2}{2\mathrm{R}}$

(3) $\frac{{\mathrm{Mv}}^2}{2(\mathrm{\gamma }-1)\mathrm{R}}$

(4) $\frac{(\mathrm{\gamma }-1){\mathrm{Mv}}^2}{2\mathrm{R}}$

On increasing number density for a gas in a vessel, the mean free path of a gas:

(1) Decreases

(2) Increases

(3) Remains same

(4) Becomes double

Two closed containers of equal volume are filled with air at pressure ${\mathrm{P}}_0$ and temperature ${\mathrm{T}}_0$. Both are connected by a narrow tube. If one of the containers is maintained at temperature ${\mathrm{T}}_0$ and the other at temperature T, then new pressure in the container will be:

1. $\frac{2{\mathrm{P}}_0\mathrm{T}}{\mathrm{T}+{\mathrm{T}}_0}$

2. $\frac{{\mathrm{P}}_0\mathrm{T}}{\mathrm{T}+{\mathrm{T}}_0}$

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

4. $\frac{\mathrm{T}+{\mathrm{T}}_0}{{\mathrm{P}}_0}$

The pressures of a gas filled in the bulb of a constant volume gas thermometer at temperatures $0°\mathrm{C}$ and $100°\mathrm{C}$ are 27.50 cm and 37.50 cm of Hg respectively. At an unknown temperature, the pressure is 32.45 cm of Hg. The unknown temperature is:

1. $30°\mathrm{C}$

2. $39°\mathrm{C}$

3. $49.5°\mathrm{C}$

4. $29.6°\mathrm{C}$