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Q. No.Given below are two statements:
| Statement I: | The average momentum of a molecule in a sample of an ideal gas depends on temperature. |
| Statement II: | The RMS speed of oxygen molecules in a gas is \(v\). If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the RMS speed will become \(2v\). |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Both Statement I and Statement II are incorrect. |
| 3. | Statement I is correct but Statement II is incorrect. |
| 4. | Statement I is incorrect but Statement II is correct. |
Subtopic: Â Types of Velocities |
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Given below are two statements:
| Assertion (A): | The average velocity of the molecules of an ideal gas increases when the temperature rises. |
| Reason (R): | The internal energy of an ideal gas increases with temperature, and this internal energy is the random kinetic energy of molecular motion. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Â Types of Velocities |
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On the basis of the kinetic theory of gases, one compares \(1~\text{gm}\) of hydrogen with \(1~\text{gm}\) of argon both at \(0^\circ \text{C}.\) Then:
| 1. | the same temperature implies that the average kinetic energy of the molecules is the same in both cases. |
| 2. | the same temperature implies that the average potential energy of the molecules is the same in both cases. |
| 3. | the internal energies in both cases are equal. |
| 4. | when both the samples are heated by \(1^\circ \text{C},\) the total energy added to both of them is the same. |
Subtopic: Â Kinetic Energy of an Ideal Gas |
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Given below are two statements:
| Statement I: | In an ideal gas, all the molecules move with the same RMS speed but in different directions. |
| Statement II: | The molecules of an ideal gas undergo random elastic collisions with the walls of the container. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Â Types of Velocities |
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Match the \(C_p/C_V\) ratio for ideal gases with different type of molecules :
| Column I | Column II | ||
| (A) | Monatomic | (I) | \(7/5\) |
| (B) | Diatomic rigid molecules | (II) | \(9/7\) |
| (C) | Diatomic non-rigid molecules | (III) | \(4/3\) |
| (D) | Triatomic rigid molecules | (IV) | \(5/3\) |
| 1. | (A)-(III), (B)-(IV), (C)-(II), (D)-(I) |
| 2. | (A)-(II), (B)-(III), (C)-( I), (D)-(IV) |
| 3. | (A)-(IV), (B)-(II), (C)-(I), (D)-(III) |
| 4. | (A)-(IV), (B)-(I), (C)-(II), (D)-(III) |
Subtopic: Â Law of Equipartition of Energy |
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Which one of the following schematic graphs best represents the variation of \(PV\) (in joules) versus \(T\) (in kelvin) of one mole of an ideal gas? (The dotted line represents \(PV=T\)).
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â Ideal Gas Equation |
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Given below are two statements:
| Assertion (A): | The translational kinetic energy of every molecule of an ideal gas increases by \(50\%,\) if the absolute temperature is raised by \(50\text{%}.\) |
| Reason (R): | The average translational kinetic energy of the molecules of an ideal gas is directly proportional to its absolute temperature. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Â Kinetic Energy of an Ideal Gas |
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Consider the following statements for air molecules in an airtight container:
| I. | the average speed of molecules is larger than the root mean square speed. |
| II. | the mean free path of molecules is larger than the mean distance between molecules. |
| III. | the mean free path of molecules increases with temperature. |
| IV. | the RMS speed of a nitrogen molecule is smaller than an oxygen molecule. |
The true statements are:
| 1. | only II |
| 2. | II and III |
| 3. | II and IV |
| 4. | I, II, and IV |
Subtopic: Â Mean Free Path |
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An ideal gas is confined in a closed container and slowly heated. As the temperature rises, which of the following statements are correct?
| (A) | The mean free path of gas molecules decreases. |
| (B) | The mean collision time between the molecules decreases. |
| (C) | The mean free path remains unchanged. |
| (D) | The mean collision time remains unchanged. |
Choose the correct option from the given ones:
| 1. | (C) and (D) only |
| 2. | (A) and (B) only |
| 3. | (A) and (D) only |
| 4. | (B) and (C) only |
Subtopic: Â Mean Free Path |
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The average momentum of the molecules in a sample of \(H_2\) - gas at temperature 300 K has a magnitude \(p_1\) and that for He-gas at the same temperature has the magnitude \(p_2.\) Then,
| 1. | \(p_1 > p_2\) |
| 2. | \(p_2 > p_1\) |
| 3. | \(p_1 = p_2\) |
| 4. | the relationship between \(p_1\) and \(p_2\) depends on pressure. |
Subtopic: Â Types of Velocities |
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