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Q. No.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: Kinetic Energy of an Ideal Gas |
55%
Level 3: 35%-60%
Hints
The volume occupied by the molecules contained in \(4.5~\text{kg}\) water at STP, if the molecular forces vanish away, is:
1. \(5.6~\text{m}^3\)
2. \(5.6\times10^{6}~\text{m}^3\)
3. \(5.6\times10^{3}~\text{m}^3\)
4. \(5.6\times10^{-3}~\text{m}^3\)
1. \(5.6~\text{m}^3\)
2. \(5.6\times10^{6}~\text{m}^3\)
3. \(5.6\times10^{3}~\text{m}^3\)
4. \(5.6\times10^{-3}~\text{m}^3\)
Subtopic: Ideal Gas Equation |
Level 3: 35%-60%
NEET - 2022
Hints
Given below are two statements:
| Assertion (A): | The molecules of a monoatomic gas has three degrees of freedom. |
| Reason (R): | The molecules of diatomic gas have five degrees of freedom. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Law of Equipartition of Energy |
93%
Level 1: 80%+
Hints
Given below are two statements:
| Assertion (A): | The molar heat capacity of the gas can have any value from \(-\infty\) to \(\infty\). |
| Reason (R): | The molar heat capacity of the gas for the isothermal process is \(\infty\). |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Specific Heat |
64%
Level 2: 60%+
Hints
A gas has \(n\) degrees of freedom. The ratio of the specific heat of the gas at constant volume to the specific heat of the gas at constant pressure will be:
| 1. | \({\dfrac{n} {n+2}}\) | 2. | \({\dfrac{n+2} {n}}\) |
| 3. | \({\dfrac{n} {2n+2}}\) | 4. | \({\dfrac{n} {n-2}}\) |
Subtopic: Specific Heat |
72%
Level 2: 60%+
JEE
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Hints
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A vessel contains \(16\) g of hydrogen and \(128\) g of oxygen at standard temperature and pressure. The volume of the vessel in cm3 is:
1. \(72\times10^{5}\)
2. \(32\times10^{5}\)
3. \(27\times10^{4}\)
4. \(54\times10^{4}\)
1. \(72\times10^{5}\)
2. \(32\times10^{5}\)
3. \(27\times10^{4}\)
4. \(54\times10^{4}\)
Subtopic: Ideal Gas Equation |
75%
Level 2: 60%+
JEE
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Hints
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The Earth’s atmosphere contains both oxygen and nitrogen. The mass of an oxygen molecule is greater than that of a nitrogen molecule. On a certain day, the temperature of air in a room is \(300~\text{K}.\)
Consider the following statements regarding the motion of oxygen and nitrogen molecules:
| (A) | Both gases have the same mean square velocity \((\overline{v^2}). \) |
| (B) | Nitrogen molecules have a greater mean square velocity \((\overline{v^2}) \) than oxygen molecules. |
| (C) | Nitrogen molecules have a greater mean kinetic energy than oxygen molecules. |
| (D) | Oxygen molecules have a greater mean kinetic energy than nitrogen molecules. |
1. (A) only
2. (A) and (C) only
3. (B) and (D) only
4. (B) only
Subtopic: Types of Velocities |
71%
Level 2: 60%+
Hints
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%
Level 2: 60%+
JEE
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Hints
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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%
Level 1: 80%+
JEE
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Hints
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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 |
74%
Level 2: 60%+
JEE
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Hints
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