Kinetic Theory

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is :

1. The root mean square speed of sulfur hexafluoride is the largest
2. All vessels contain unequal number of respective molecules
3. The root mean square speed of molecules is same in all three cases
4. The root mean square speed of helium is the largest

Match Column - I and Column - II and choose the correct match from the given choices.

1. (A) - (R), (B) - (Q), (C) - (P), (D) - (S)
2. (A) - (R), (B) - (P), (C) - (S), (D) - (Q)
3. (A) - (Q), (B) - (R), (C) - (S), (D) - (P)
4. (A) - (Q), (B) - (P), (C) - (S), (D) - (R)

The average thermal energy for a mono-atomic gas is : (kB is Boltzmann constant and T absolute temperature)

1. 32kBT
2. 52kBT
3. 72kBT
4. 12kBT

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