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

Column - I Column - II
(A) Root mean square speed of gas molecules (P) 13nmv¯2
(B) Pressure exerted by ideal gas (Q) 3RTM
(C) Average kinetic energy of a molecule (R) 52RT
(D) Total internal energy of 1 mole of a diatomic gas (S) 32kBT
 
(A) (B) (C) (D)
1. (Q) (P) (S) (R)
2. (R) (Q) (P) (S)
3. (R) (P) (S) (Q)
4. (Q) (R) (S) (P)
Subtopic:  Kinetic Energy of an Ideal Gas |
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The mean free path for a gas, with molecular diameter d and number density n, can be expressed as:
1. 12nπd2
2. 12n2πd2
3. 12n2π2d2
4. 12nπd

Subtopic:  Mean Free Path |
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A cylinder contains hydrogen gas at a pressure of 249 kPa and temperature 27°C. 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

Subtopic:  Ideal Gas Equation |
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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

Subtopic:  Kinetic Energy of an Ideal Gas |
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The mean free path l for a gas molecule depends upon the diameter, d of the molecule as:

1.  l 1d2

2.  l d

3.  l  d2

4.  l 1d

Subtopic:  Mean Free Path |
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An ideal gas equation can be written as P=ρRTM0 where ρ and M0 are respectively, 

1.  Mass density, the mass of the gas 

2.  Number density, molar mass 

3.  Mass density, molar mass 

4.  Number density, the mass of the gas 

Subtopic:  Ideal Gas Equation |
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An increase in temperature of a gas-filled in a container would lead to:

1. decrease in intermolecular distance.

2. increase in its mass.

3. increase in its kinetic energy.

4. decrease in its pressure.

Subtopic:  Law of Equipartition of Energy |
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The value γ=CpCv for hydrogen, helium, and another ideal diatomic gas X (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:

1. 75, 53, 97

2. 53, 75, 97

3. 53, 75, 75

4. 75, 53, 75

Subtopic:  Law of Equipartition of Energy |
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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 x 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

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

1. 15 RT

2. 9 RT

3. 11 RT

4. 4 RT

Subtopic:  Law of Equipartition of Energy |
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