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Q. No.Given below are two statements:
Statement I:
In an ideal gas, all the molecules move with the same RMS speed but in different directions.
Statement II:
The molecules of an ideal gas undergo random elastic collisions with the walls of the container.
1.
Statement I is incorrect and Statement II is correct.
2.
Both Statement I and Statement II are correct.
3.
Both Statement I and Statement II are incorrect.
4.
Statement I is correct and Statement II is incorrect.
Subtopic: Â Types of Velocities |
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An ideal gas at absolute temperature \(T\) is contained in a cubical vessel of side \(L.\) The average momentum of the gas molecules, in a direction parallel to a side of the vessel, is:
| 1. | \(\propto T\) | 2. | \(\propto\sqrt T\) |
| 3. | \(T^{-1/2}\) | 4. | zero |
Subtopic: Â Kinetic Energy of an Ideal Gas |
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The molar heat capacity of an ideal gas:
| 1. | is \(\dfrac32 R\) |
| 2. | \(\geq\)\(\dfrac32 R\) |
| 3. | \(\leq\)\(\dfrac32 R\) |
| 4. | can have any value depending on the process |
Subtopic: Â Specific Heat |
 51%
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The temperature of a mono-atomic gas is measured by indirectly measuring the RMS speed of its molecules \(v_r.\) The gas is enclosed in a cubical vessel of side-\(L,\) and this gas expands adiabatically with the side-\(L\) expanding. During the process:
| 1. | \(v_r~L^{1/3}=\text{constant}\) | 2. | \(v_r~L^{2}=\text{constant}\) |
| 3. | \(v_r~L=\text{constant}\) | 4. | \({\large\dfrac{v_r}{L}}=\text{constant}\) |
Subtopic: Â Types of Velocities |
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The average internal kinetic energy, due to translational motion of a molecule in an ideal gas at absolute temperature \(T,\) is \(E_{tr}.\) This quantity, \(E_{tr},\) depends on:
Choose the correct option from the given ones:
| (A) | mass of a molecule |
| (B) | number of atoms in a molecule |
| (C) | temperature, \(T\) |
Choose the correct option from the given ones:
| 1. | (C) | 2. | (B) |
| 3. | (B), (C) | 4. | (A), (B), (C) |
Subtopic: Â Kinetic Energy of an Ideal Gas |
 54%
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An equimolar mixture of nitrogen and carbon dioxide gases is cooled until the carbon dioxide gas condenses. Assume that the volume of liquid \(CO_2\) is negligible compared to \(CO_2\) gas which behaves ideally. Before the gas condensed, the total pressure was \(P_1\) and after condensation the total pressure was \(P_2.\) The change in temperature is negligible. Then:
| 1. | \(P_1=P_2\) | 2. | \(P_1=2P_2\) |
| 3. | \(\Large\frac{P_1}{28}= \frac{P_2}{44}\) | 4. | \(28P_1=44P_2\) |
Subtopic: Â Ideal Gas Equation |
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The molar specific heat capacity (at constant pressure) of a monoatomic gas is \(C_1,\) of a diatomic gas is \(C_2;\) and of an equimolar mixture of the two is \(C_3.\) Then:
| 1. | \(C_1>C_3>C_2\) | 2. | \(C_1>C_2>C_3\) |
| 3. | \(C_1<C_3<C_2\) | 4. | \(C_1<C_2<C_3\) |
Subtopic: Â Specific Heat |
 50%
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A molecule of helium \((He),\) having a speed equal to the RMS speed at a temperature of \(400~\text K,\) is introduced into hydrogen gas \((H_2)\) at \(300~\text K.\) After sufficient time (and collisions with the hydrogen gas molecules), the speed of the helium molecule will (on average):
1. increase
2. decrease
3. remain the same
4. become zero
1. increase
2. decrease
3. remain the same
4. become zero
Subtopic: Â Kinetic Energy of an Ideal Gas |
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Given below are two statements:
| Statement I: | The average momentum of a molecule in a sample of an ideal gas depends on temperature. |
| Statement II: | The RMS speed of oxygen molecules in a gas is \(v\). If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the RMS speed will become \(2v\). |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Both Statement I and Statement II are incorrect. |
| 3. | Statement I is correct but Statement II is incorrect. |
| 4. | Statement I is incorrect but Statement II is correct. |
Subtopic: Â Types of Velocities |
From NCERT
JEE
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Hints
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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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