If m represents the mass of each molecule of a gas and T, its absolute temperature, then the root mean square velocity of the gaseous molecule is proportional to

• mT

• m^1/2T^1/2

• m^-1/2T

• m^-1/2T^1/2

12.

A molecule of a gas has six degrees of freedom. Then, the molar specific heat of the gas at constant volume is

• $\frac{\mathrm{R}}{2}$

• R

• 3R

• 2R

Total number of degrees of freedom of a rigid diatomic molecule is

• 3

• 6

• 5

• 2

If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature

• is doubled

• becomes one-fourth

• remains constant

• is halved

The ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is

• $\frac{7}{2}$

• $\frac{3}{2}$

• $\frac{3}{5}$

• $\frac{7}{5}$

The temperature at which oxygen molecules have the same root mean square speed as that of hydrogen molecules at 300 K is

• 600 K

• 2400 K

• 4800 K

• 300 K

Mean free path of a gas molecule is

• inversely proportional to number of molecules per unit volume

• inversely proportional to diameter of the molecule

• directly proportional to the square root of the absolute temperature

• directly proportional to the molecular mass

In a certain region of space there are only 5 molecules per cm³ on an average. The temperature there is 3 K.The pressure of this dilute gas is  (k = 1.38 x 10^-23 J/K)

• 20.7 × 10^-17 N/m²

• 15.3 × 10^-15 N/m²

• 2.3 × 10^-10 N/m²

• 5.3 × 10^-5 N/m²

The value of $\frac{\mathrm{PV}}{\mathrm{T}}$ for one mole of an ideal gas is nearly equal to

• 2 J mol^-1 K^-1

• 8.3 mol^-1 K^-1

• 4.2 mol^-1 K^-1

• 2 cal mol^-1 K^-1

If P is the pressure, V the volume, R the gas constant, k the Boltzmann constant and T the absolute temperature, then the number of molecules in the given mass of the gas is given by

• $\frac{\mathrm{PV}}{\mathrm{RT}}$

• $\frac{\mathrm{PV}}{\mathrm{kT}}$

• $\frac{\mathrm{PR}}{\mathrm{T}}$

• pV