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Q. No.The energy of a gas molecule in a gas at a given temperature \(T~(\text{K})\) is calculated based on the kinetic theory of gases. Match Column-I with Column-II.
| Column-I | Column-II | ||
| (A) | mean kinetic energy per mole of diatomic gas | (P) | \(\dfrac{3}{2}k_BT\) |
| (B) | mean transitional kinetic energy per molecule of a gas | (Q) | \(\dfrac{3}{2}RT\) |
| (C) | mean translational kinetic energy per mole of an ideal gas | (R) | \(\dfrac{5}{2}RT\) |
| (D) | mean rotational kinetic energy per molecule of diatomic gas | (S) | \(k_BT\) |
| 1. | A(P), B(R), C(S), D(Q) |
| 2. | A(R), B(Q), C(P), D(S) |
| 3. | A(R), B(S), C(Q), D(P) |
| 4. | A(R), B(P), C(Q), D(S) |
Subtopic: Kinetic Energy of an Ideal Gas |
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The ratio of specific heats \(\left (\dfrac{C_p}{C_v}\right)\) in terms of degree of freedom \((f)\) is given by:
| 1. | \(\left(1+\dfrac{f}{3}\right) \) | 2. | \(\left(1+\dfrac{2}{f}\right)\) |
| 3. | \(\left(1+\dfrac{f}{2}\right) \) | 4. | \(\left(1+\dfrac{1}{f}\right)\) |
Subtopic: Law of Equipartition of Energy |
88%
From NCERT
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One mole of a monoatomic gas is mixed with three moles of a diatomic gas. If the molecular specific heat of the mixture at constant volume is \(\dfrac{\alpha^2}{4} {R}~ \text{J} / \text{mol-K},\) then the value of \(\alpha\) will be:
(assume that the given diatomic gas has no vibrational mode)
(assume that the given diatomic gas has no vibrational mode)
| 1. | \(5\) | 2. | \(4\) |
| 3. | \(3\) | 4. | \(2\) |
Subtopic: Specific Heat |
74%
From NCERT
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The Earth’s atmosphere contains oxygen and nitrogen. The mass of an oxygen molecule is greater than the mass of a nitrogen molecule. The temperature of the air in a room on a particular day is \(300~\text{K}.\) Below are four statements about the motion of the two types of molecules in this room.
Which of the statements is/are correct?
| A. | They have an equal mean square velocity \((\overline{v^2}).\) |
| B. | A nitrogen molecule has a greater mean square velocity \((\overline{v^2})\) than an oxygen molecule. |
| C. | A nitrogen molecule has a greater mean kinetic energy than an oxygen molecule. |
| D. | An oxygen molecule has a greater mean kinetic energy than a nitrogen molecule. |
Which of the statements is/are correct?
| 1. | Statement A only |
| 2. | Statement A and C only |
| 3. | Statement B and D only |
| 4. | Statement B only |
Subtopic: Types of Velocities |
72%
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Choose the correct option regarding ideal gas:
| 1. | in \(P={\dfrac{m}{M}}RT\), \(m\) is the mass of gas per unit volume. |
| 2. | in \(P={\dfrac{m}{M}}RT\), \(m\) is the mass of one molecule of gas. |
| 3. | in \(P=\dfrac{1}{3} \dfrac{m N}{V} v_{r m s}^2\), \(m\) is the total mass of gas. |
| 4. | in \(v_{r m s}=\sqrt{\dfrac{3 k T}{m}}\), \(m\) is the total mass of the gas. |
Subtopic: Ideal Gas Equation |
52%
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Which of the following graphs, shows the variation of the mean kinetic energy \(E\) of an ideal gas molecule with temperature
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Kinetic Energy of an Ideal Gas |
From NCERT
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The mean free path of gas molecules depends on:
(\(d=\) molecular diameter)
1. \(d\)
2. \(d^2\)
3. \(d^{-2}\)
4. \(d^{-1}\)
Subtopic: Mean Free Path |
83%
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The average energy of a molecule for each degree of freedom is:
| 1. | \(\dfrac{3}{2} kT\) | 2. | \(\dfrac{kT}{2}\) |
| 3. | \(\dfrac{3}{4} kT\) | 4. | \(kT\) |
Subtopic: Law of Equipartition of Energy |
57%
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The molar-specific heat capacity at constant volume for a rigid diatomic molecule is:
(\(R\) is the universal gas constant)
(\(R\) is the universal gas constant)
| 1. | \({\dfrac 9 7}R\) | 2. | \({\dfrac7 2}R\) |
| 3. | \({\dfrac 5 2}R\) | 4. | \({\dfrac 3 2}R\) |
Subtopic: Specific Heat |
81%
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If the pressure in a closed vessel is reduced by removing some of the gas, how is the mean free path between two gas molecules affected?
| 1. | It increases. |
| 2. | It decreases. |
| 3. | It remains unchanged. |
| 4. | It increases or decreases depending on the nature of the gas. |
Subtopic: Mean Free Path |
67%
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