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Q. No.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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JEE
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Consider a gas of triatomic molecules. The molecules are assumed to be triangular, composed of massless rigid rods with atoms at the vertices. The internal energy of a mole of the gas at temperature \(T\) is:
| 1. | \( 3 R T \) | 2. | \(\dfrac{5}{2} R T \) |
| 3. | \( \dfrac{9}{2} R T \) | 4. | \( \dfrac{3}{2} R T \) |
Subtopic: Â Law of Equipartition of Energy |
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JEE
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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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The pressure of an ideal gas is written as \(p=\dfrac{2E}{3V},\) where \(E\) is the total kinetic energy, and \(V\) is the volume.
This statement is:
| 1. | always true. |
| 2. | true for mono-atomic gases. |
| 3. | always false. |
| 4. | true for diatomic gases. |
Subtopic: Â Kinetic Energy of an Ideal Gas |
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From NCERT
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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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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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