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Q. No.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
Subtopic: Â Specific Heat |
 61%
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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 |
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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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%
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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 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): | 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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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%
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