Match **column - I** and **column - I**I 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 $27\xb0\mathrm{C.}$Its density is: (R = 8.3 J $mo{l}^{-1}{K}^{-1}$)

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. $l\propto \frac{1}{{d}^{2}}$

2. $l\propto d$

3. $l\propto {d}^{2}$

4. $l\propto \frac{1}{d}$

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. $\frac{7}{5},\frac{5}{3},\frac{9}{7}$

2. $\frac{5}{3},\frac{7}{5},\frac{9}{7}$

3. $\frac{5}{3},\frac{7}{5},\frac{7}{5}$

4. $\frac{7}{5},\frac{5}{3},\frac{7}{5}$

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 k_{B} = 1.38 × 10^{-23} J K^{-1}):

1. $2.508\times {10}^{4}K$

2. $8.360\times {10}^{4}K$

3. $5.016\times {10}^{4}K$

4. $1.254\times {10}^{4}K$

Subtopic: Types of Velocities |

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A gas mixture consists of 2 moles of O_{2} 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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