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Q. No.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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Given below are two statements:
| Assertion (A): | As a gas bubble rises from the bottom of a lake, its volume decreases. |
| Reason (R): | As the gas bubble rises from the bottom of a lake, the pressure of the gas within decreases. |
| 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 Ideal Gas Equation |
 69%
From NCERT
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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 |
 57%
From NCERT
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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 |
 56%
From NCERT
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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 |
 61%
From NCERT
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The ratio of the \(\text{RMS}\) speed \((v_\text{RMS})\) of the molecules of an ideal gas to the speed of sound \((v_s)\) in the gas, i.e. \({\dfrac{v_\text{RMS}}{v_s}}{\small=}\)
| 1. | \(\dfrac{3}{\gamma}\) | 2. | \(\sqrt{\dfrac{3}{\gamma}}\) |
| 3. | \(\dfrac{\gamma}{3}\) | 4. | \(\sqrt{\dfrac{\gamma}{3}}\) |
Subtopic: Â Types of Velocities |
 80%
From NCERT
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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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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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Suppose that the average kinetic energy (translational & rotational) of random molecular motion of helium (\(He\)) at temperature \(T_{He}\) is equal to that of hydrogen (\(H_2\)) at temperature \(T_{H_2}\). Then,
| 1. | \(T_{H_{2}}=T_{H e}\) | 2. | \(\dfrac{T_{H_2}}{2}=\dfrac{T_{He}}{4}\) |
| 3. | \(5 T_{H_2}=3 T_{He}\) | 4. | \(\dfrac{T_{H_{2}}}{5}=\dfrac{T_{{He }}}{3}\) |
Subtopic: Â Kinetic Energy of an Ideal Gas |
 54%
From NCERT
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