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) $\frac{1}{3}nm{\overline{v}}^{2}$ (B) Pressure exerted by ideal gas (Q) $\sqrt{\frac{3RT}{M}}$ (C) Average kinetic energy of a molecule (R) $\frac{5}{2}RT$ (D) Total internal energy of 1 mole of a diatomic gas (S) $\frac{3}{2}{k}_{B}T$

 (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. $\frac{1}{\sqrt{2}n{\mathrm{\pi d}}^{2}}$
2. $\frac{1}{\sqrt{2}{n}^{2}{\mathrm{\pi d}}^{2}}$
3. $\frac{1}{\sqrt{2}{n}^{2}{\pi }^{2}{d}^{2}}$
4. $\frac{1}{\sqrt{2}n\mathrm{\pi d}}$

Subtopic:  Mean Free Path |
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A cylinder contains hydrogen gas at a pressure of 249 kPa and temperature Its density is: (R = 8.3 J )

1.  0.2 $kg/{m}^{3}$

2.  0.1 $kg/{m}^{3}$

3.  0.02 $kg/{m}^{3}$

4.  0.5 $kg/{m}^{3}$

Subtopic:  Ideal Gas Equation |
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The average thermal energy for a mono-atomic gas is:

(${\mathrm{k}}_{\mathrm{B}}$ is Boltzmann constant and T absolute temperature)

1. $\frac{3}{2}{k}_{\mathrm{B}}\mathrm{T}$

2. $\frac{5}{2}{k}_{\mathrm{B}}\mathrm{T}$

3. $\frac{7}{2}{k}_{\mathrm{B}}\mathrm{T}$

4. $\frac{1}{2}{k}_{\mathrm{B}}\mathrm{T}$

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.

2.

3.

4.

Subtopic:  Mean Free Path |
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An ideal gas equation can be written as $\mathrm{P}=\frac{\mathrm{\rho RT}}{{\mathrm{M}}_{0}}$ where $\mathrm{\rho }$ and ${\mathrm{M}}_{0}$ 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 $\mathrm{\gamma }=\left(\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}\right)$ 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.

2.

3.

4.

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.

3.

4.

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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