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Q. No.The temperature of a gas is \(-50^\circ \text{C}.\) To what temperature the gas should be heated so that the RMS speed is increased by \(3\) times?
1.
\(223~\text{K}\)
2.
\(669^\circ \text{C}\)
3.
\(3295^\circ \text{C}\)
4.
\(3097~\text{K}\)
Subtopic: Types of Velocities |
53%
From NCERT
NEET - 2023
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A gas in a vessel is initially at pressure \(P.\) If the mass of all the gas molecules is halved and their speed is doubled, then the resultant pressure will be:
| 1. | \(2 P\) | 2. | \(P\) |
| 3. | \(\dfrac{P}{2}\) | 4. | \(4 P\) |
Subtopic: Kinetic Energy of an Ideal Gas |
66%
From NCERT
NEET - 2013
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The amount of heat energy required to raise the temperature of \(1~\text {gram}\) of helium at constant volume from \(T_1~\text K\) to \(T_2~\text K\) is:
| 1. | \(\dfrac{3}{4} N_A k_B\left(T_2-T_1\right)\) | 2. | \(\dfrac{2}{3} N_A k_B\left(T_2-T_1\right)\) |
| 3. | \(\dfrac{3}{2} N_A k_B\left(T_2-T_1\right)\) | 4. | \(\dfrac{3}{8} N_A k_B\left(T_2-T_1\right)\) |
Subtopic: Law of Equipartition of Energy |
61%
From NCERT
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Choose the correct option regarding ideal gas:
| 1. | in \(P={\dfrac{m}{M}}RT\), \(m\) is the mass of gas per unit volume. |
| 2. | in \(P={\dfrac{m}{M}}RT\), \(m\) is the mass of one molecule of gas. |
| 3. | in \(P=\dfrac{1}{3} \dfrac{m N}{V} v_{r m s}^2\), \(m\) is the total mass of gas. |
| 4. | in \(v_{r m s}=\sqrt{\dfrac{3 k T}{m}}\), \(m\) is the total mass of the gas. |
Subtopic: Ideal Gas Equation |
52%
From NCERT
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The energy of a gas molecule in a gas at a given temperature \(T~(\text{K})\) is calculated based on the kinetic theory of gases. Match Column-I with Column-II.
| Column-I | Column-II | ||
| (A) | mean kinetic energy per mole of diatomic gas | (P) | \(\dfrac{3}{2}k_BT\) |
| (B) | mean transitional kinetic energy per molecule of a gas | (Q) | \(\dfrac{3}{2}RT\) |
| (C) | mean translational kinetic energy per mole of an ideal gas | (R) | \(\dfrac{5}{2}RT\) |
| (D) | mean rotational kinetic energy per molecule of diatomic gas | (S) | \(k_BT\) |
| 1. | A(P), B(R), C(S), D(Q) |
| 2. | A(R), B(Q), C(P), D(S) |
| 3. | A(R), B(S), C(Q), D(P) |
| 4. | A(R), B(P), C(Q), D(S) |
Subtopic: Kinetic Energy of an Ideal Gas |
67%
From NCERT
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The molar-specific heat capacity at constant volume for a rigid diatomic molecule is:
(\(R\) is the universal gas constant)
(\(R\) is the universal gas constant)
| 1. | \({\dfrac 9 7}R\) | 2. | \({\dfrac7 2}R\) |
| 3. | \({\dfrac 5 2}R\) | 4. | \({\dfrac 3 2}R\) |
Subtopic: Specific Heat |
81%
From NCERT
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Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following, is:
| 1. | All vessels contain an unequal number of respective molecules. |
| 2. | The root mean square speed of molecules is the same in all three cases. |
| 3. | The root mean square speed of helium is the largest. |
| 4. | The root mean square speed of sulfur hexafluoride is the largest. |
Subtopic: Types of Velocities |
74%
From NCERT
NEET - 2022
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A flask contains argon and oxygen in the ratio of \(3:2\) in mass and the mixture is kept at \(27^\circ\mathrm{C}\). The ratio of their average kinetic energy per molecule respectively will be:
1. \(3:2\)
2. \(9:4\)
3. \(2:3\)
4. \(1:1\)
1. \(3:2\)
2. \(9:4\)
3. \(2:3\)
4. \(1:1\)
Subtopic: Kinetic Energy of an Ideal Gas |
73%
From NCERT
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The ratio of specific heats \(\left (\dfrac{C_p}{C_v}\right)\) in terms of degree of freedom \((f)\) is given by:
| 1. | \(\left(1+\dfrac{f}{3}\right) \) | 2. | \(\left(1+\dfrac{2}{f}\right)\) |
| 3. | \(\left(1+\dfrac{f}{2}\right) \) | 4. | \(\left(1+\dfrac{1}{f}\right)\) |
Subtopic: Law of Equipartition of Energy |
88%
From NCERT
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One mole of a monoatomic gas is mixed with three moles of a diatomic gas. If the molecular specific heat of the mixture at constant volume is \(\dfrac{\alpha^2}{4} {R}~ \text{J} / \text{mol-K},\) then the value of \(\alpha\) will be:
(assume that the given diatomic gas has no vibrational mode)
(assume that the given diatomic gas has no vibrational mode)
| 1. | \(5\) | 2. | \(4\) |
| 3. | \(3\) | 4. | \(2\) |
Subtopic: Specific Heat |
74%
From NCERT
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