Q. No.Two ideal gases contained in vessels \(A\) and \(B\) are connected by means of a pipe, and the plug is opened so that the gases mix. The final pressure is \(P\) (atm) and the temperature is \(T\) (kelvin). Then, \(\dfrac{P}{T}=\) (numerically)
| 1. | \(\dfrac{1}{100}\) | 2. | \(\dfrac{1}{200}\) |
| 3. | \(\dfrac{1}{400}\) | 4. | none of these |
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Hydrogen gas is contained in a vessel and the RMS speed of the gas molecules is \(v\). The gas is heated isobarically so that its volume doubles, then it is compressed isothermally so that it returns to the same volume. The final RMS speed of the molecules will be:
| 1. | 2\(v\) | 2. | \(v\)/2 |
| 3. | \(v\)\(\sqrt2\) | 4. | \(v\)/\(\sqrt2\) |
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The pressure exerted by a gas enclosed within a room is due to:
| 1. | collisions of the gas molecules with the walls of the room |
| 2. | the repulsive force between molecules of the gas |
| 3. | weight of the molecules of the gas |
| 4. | angular momentum of the molecules |
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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. |
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| 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. | \(\dfrac{T_{H_{2}}}{5}=\dfrac{T_{{He }}}{3}\) |
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| 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. |
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| 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). |
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| 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. |
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| 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). |
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1. \(X\propto V\)
2. \(X\propto V^2\)
3. \(X\propto V^{\frac12}\)
4. \(X\propto V^{-\frac12}\)
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