Kinetic Theory

The mean free path for a gas, with molecular diameter d and number density n can be expressed as :

1. 1 2n d2
2. 1 2n2 d2
3. 1 2n2 2 d2
4. 1 2n d

A cylinder contains hydrogen gas at pressure 249 kPa and temperature 27 . Its density is : (R = 8.3 J mol-1 K-1)

1. 0.2 kg/m3
2. 0.1 kg/m3
3. 0.02 kg/m3
4. 0.5 kg/m3

Increase in temperature of a gas filled in a container would lead to :

1. increase in its kinetic energy
2. decrease in intermolecular distance
3. decrease in its pressure
4. increase in its mass

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given : Mass of oxygen molecule (m) = 2.76 10-26 kg, Boltzmann's constant kB = 1.38 10-23 J K-1)

1. 2.508 104 K
2. 8.360 104 K
3. 5.016 104 K
4. 1.254 104 K

A gas mixture consists of 2 moles of O2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

1. 15 RT
2. 9 RT
3. 11 RT
4. 4 RT

The molecules of a given mass of a gas have r.m.s. velocity of 200 m s-1 at 27 and 1.0 105 N m-2 pressure. When the temperature and pressure of the gas are respectively, 127 and 0.05 105 N m-2, the r.m.s. velocity of its molecules in m s-1 is

1. 100 23
2. 1003
3. 100 2
4. 400 3

A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas ?

1. P/(kT)
2. Pm/(kT)
3. P/(kTV)
4. mkT

Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is

1. 2
2. 12
3. 23
4. 34

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K-1 mol-1. If the speed of sound in this gas at NTP is 952 m s-1, then the heat capacity at constant pressure is (Take gas constant R = 8.3 J K-1 mol-1)

1. 7.0 J K-1 mol-1
2. 8.5 J K-1 mol-1
3. 8.0 J K-1 mol-1
4. 7.5 J K-1 mol-1

The ratio of the specific heats CpCv = in terms of degrees of freedom (n) is given by

1. (1 + 2n )
2. (1 + n2 )
3. (1 + 1n )
4. (1 + n3 )