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Q. No.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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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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An equimolar mixture of helium \(\mathrm{(He)}\) and hydrogen \(\mathrm{(H_2)}\) gases is kept in a vessel at a temperature of \(500~\text{K}.\) Then:
| 1. | helium and hydrogen molecules have the same kinetic energy on average. |
| 2. | RMS speeds of helium and hydrogen molecules are equal. |
| 3. | the translational kinetic energy of hydrogen and helium molecules is equal. |
| 4. | all of the above are true. |
Subtopic: Â Kinetic Energy of an Ideal Gas |
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An ideal gas undergoes a process during which the ratio \(\dfrac{V}{T^2}\) is constant. The variation of \(X=pV\) as a function of volume \(V\) is:
1. \(X\propto V\)
2. \(X\propto V^2\)
3. \(X\propto V^{\frac12}\)
4. \(X\propto V^{-\frac12}\)
1. \(X\propto V\)
2. \(X\propto V^2\)
3. \(X\propto V^{\frac12}\)
4. \(X\propto V^{-\frac12}\)
Subtopic: Â Ideal Gas Equation |
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During a certain atmospheric process, a pocket of air near the earth's surface rises upwards very rapidly into the upper regions of the atmosphere. As a result, the temperature of this air:
| 1. | increases. |
| 2. | decreases. |
| 3. | remains constant. |
| 4. | first increases, then decreases. |
Subtopic: Â Ideal Gas Equation |
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One mole of an equimolar mixture of monoatomic \((He)\) and diatomic \((H_2)\) gases is heated to raise the temperature by \(1\) K under constant pressure. The amount of heat used in this process is (nearly):
1. \(8.3\) J
2. \(16.6\) J
3. \(25\) J
4. \(29\) J
1. \(8.3\) J
2. \(16.6\) J
3. \(25\) J
4. \(29\) J
Subtopic: Â Specific Heat |
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Suppose that the average kinetic energy (translational & rotational) of random molecular motion of helium \(\mathrm{(He})\) at temperature \(T_\mathrm{He}\) is equal to that of hydrogen \(\mathrm{(H_2})\) at temperature \(T_\mathrm{H_2}.\) Then;
| 1. | \(T_\mathrm {H_{2}}=T_\mathrm{H e}\) | 2. | \(\dfrac{T_\mathrm{H_2}}{2}=\dfrac{T_\mathrm{He}}{4}\) |
| 3. | \(5 T_\mathrm{H_2}=3 T_\mathrm{He}\) | 4. | \(\dfrac{T_\mathrm{H_{2}}}{5}=\dfrac{T_\mathrm{{He }}}{3}\) |
Subtopic: Â Kinetic Energy of an Ideal Gas |
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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 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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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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