Q. No.For a given at \(1\) atm pressure, the rms speed of the molecules is \(200~\text{m/s}\) at \(127^\circ\text{C}.\) At \(2\) atm pressure and at \(227^\circ\text{C},\) the rms speed of the molecules will be:
| 1. | \(100~\text{m/s}\) | 2. | \(80\sqrt{5}~\text{m/s}\) |
| 3. | \(100\sqrt{5}~\text{m/s}\) | 4. | \(80~\text{m/s}\) |
Subtopic: Types of Velocities |
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Nitrogen gas is at a certain temperature \(300^\circ \text{C}.\) At what temperature (in Kelvin) will the root mean square (rms) speed of a hydrogen molecule be equal to the rms speed of a nitrogen molecule?
(Given: molar mass of nitrogen molecule is \(28~\text g/ \text{mol}\) and molar mass of hydrogen molecule is \(2~\text g/ \text{mol}\))
1. \(21\) K
2. \(41\) K
3. \(52\) K
4. \(76\) K
Subtopic: Types of Velocities |
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The root mean square speed of molecules of a given mass of a gas at \(27^\circ \text{C}\) and \(1~\text{atm}\) is \(200~\text{m/s}\) The root mean square speed of molecules of the gas at \(127^\circ \text{C}\) and \(2~\text{atm}\) will be:
| 1. | \(\dfrac{200}{\sqrt{3}}~\text{m/s}\) | 2. | \(\dfrac{200}{\sqrt{5}}~\text{m/s}\) |
| 3. | \(\dfrac{400}{\sqrt{3}}~\text{m/s}\) | 4. | \(\dfrac{100}{\sqrt{5}}~\text{m/s}\) |
Subtopic: Types of Velocities |
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The relation between root mean square speed (vrms) and most probable speed (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be:
1. \(\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{2}{3}} \mathrm{v}_{\mathrm{p}} \)
2. \(\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3}{2}} \mathrm{v}_{\mathrm{p}} \)
3. \(\text v_{rms} = \text v_p\)
4. \(\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{1}{3}} \mathrm{v}_{\mathrm{P}}\)
1. \(\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{2}{3}} \mathrm{v}_{\mathrm{p}} \)
2. \(\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3}{2}} \mathrm{v}_{\mathrm{p}} \)
3. \(\text v_{rms} = \text v_p\)
4. \(\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{1}{3}} \mathrm{v}_{\mathrm{P}}\)
Subtopic: Types of Velocities |
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What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and the oxygen molecule dissociates into atomic oxygen?
| 1. | The velocity of atomic oxygen remains the same. |
| 2. | The velocity of atomic oxygen doubles. |
| 3. | The velocity of atomic oxygen becomes half. |
| 4. | The velocity of atomic oxygen becomes four times. |
Subtopic: Types of Velocities |
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Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1:4,\) then;
Choose the correct one from the given options:
| (A) | The RMS velocity of gas molecules in two vessels will be the same. |
| (B) | The ratio of pressure in these vessels will be \(1:4\) |
| (C) | The ratio of pressure will be \(1:1\) |
| (D) | The RMS velocity of gas molecules in two vessels will be in the ratio of \(1:4\) |
| 1. | (A) and (C) only | 2. | (B) and (D) only |
| 3. | (A) and (B) only | 4. | (C) and (D) only |
Subtopic: Types of Velocities |
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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: Types of Velocities |
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The root mean square speed of smoke particles of mass 5 × 10–17 kg in their Brownian motion in air at NTP is, approximately:
[Given k = 1.38 × 10–23 JK–1 ]
1. 60 mm s–1
2. 12 mm s–1
3. 15 mm s–1
4. 36 mm s–1
[Given k = 1.38 × 10–23 JK–1 ]
1. 60 mm s–1
2. 12 mm s–1
3. 15 mm s–1
4. 36 mm s–1
Subtopic: Types of Velocities |
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If \(T\) is the temperature of a gas, then RMS velocity of the gas molecules is proportional to:
1. \(T^{\frac{1}{2}}\)
2. \(T^{-\frac{1}{2}}\)
3. \(T\)
4. \(T^2\)
1. \(T^{\frac{1}{2}}\)
2. \(T^{-\frac{1}{2}}\)
3. \(T\)
4. \(T^2\)
Subtopic: Types of Velocities |
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What would be the ratio of the root mean square speed of oxygen gas molecules to that of hydrogen gas molecules, if the temperature of both the gases are the same?
| 1. | \(1:4\) | 2. | \(1:16\) |
| 3. | \(1:32\) | 4. | \(1:8\) |
Subtopic: Types of Velocities |
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