Kinetic Theory · Question 2

The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If number densities of the gases A and B are nA and nB, respectively, the correct option is:

1. nA = 12 nB
2. nA = nB
3. nA = 2nB
4. nA = 14 nB

A container has two chambers of volumes V1 = 2 litres and V2 = 3 litres separated by a partition made of a thermal insulator. The chambers contain n1 = 5 and n2 = 4 moles of ideal gas at pressures p1 = 1 atm and p2 = 2 atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of

1. 1.4 atm
2. 1.8 atm
3. 1.3 atm
4. 1.6 atm

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressures at temperature 27 . The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given, R = 10012 J mol-1 K-1, and molecular mass of O2 = 32, 1 atm pressure = 1.01 105 N/m2]

1. 0.116 kg
2. 0.156 kg
3. 0.125 kg
4. 0.144 kg

The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures P1, P2 and P3 compared with those of Charles's law represented as dotted lines. [figure] Then the correct relation is :

1. P3 > P2 > P1
2. P1 > P3 > P2
3. P2 > P1 > P3
4. P1 > P2 > P3

According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant = CPCV is (CP and CV are the specific heat capacities of the gas at constant pressure and constant volume, respectively):

1. 4 + 3 - 1
2. 3 + 4 - 1
3. 4 - 3 - 1
4. 3 - 4 - 1

The temperature of a gas is -50 . To what temperature the gas should be heated so that the rms speed is increased by 3 times?

1. 3295
2. 3097 K
3. 223 K
4. 669

The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is

1. 5.6 106 m3
2. 5.6 103 m3
3. 5.6 10-3 m3
4. 5.6 m3

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