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Q. No.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. \(T^2\)
Subtopic: Types of Velocities |
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In a lake of depth \(40~\text{m}\) a bubble is at the bottom. Assuming the temperature and density of lake water to be uniform. What will be the density of air in the bubble?
(assume temperature \(T=12^\circ \text{C}\) and density water \(=10^3~\text{kg/m}^3,\) molecular weight of air = \(30~\text{g}\))
1. \(16.76~\text{kg/m}^3\)
2. \(15.32~\text{kg/m}^3\)
3. \(6.33~\text{kg/m}^3 \)
4. \(45.94~\text{kg/m}^3\)
(assume temperature \(T=12^\circ \text{C}\) and density water \(=10^3~\text{kg/m}^3,\) molecular weight of air = \(30~\text{g}\))
1. \(16.76~\text{kg/m}^3\)
2. \(15.32~\text{kg/m}^3\)
3. \(6.33~\text{kg/m}^3 \)
4. \(45.94~\text{kg/m}^3\)
Subtopic: Ideal Gas Equation |
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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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The average speed of N2 at \(27^\circ \mathrm{C}\) is:
1. 476 m/s
2. 470 m/s
3. 480 m/s
4. 490 m/s
1. 476 m/s
2. 470 m/s
3. 480 m/s
4. 490 m/s
Subtopic: Types of Velocities |
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In a mixture, \(0.5\) moles of \(\mathrm{O_2}\) and \(4\) moles of \(\mathrm{Ne}\) gas are taken at temperature \(T\). The internal energy of the system is equal to:
1. \(\left ( \dfrac{13}{2} \right )RT\)
2. \(\left ( \dfrac{11}{4} \right )RT\)
3. \(\left ( \dfrac{29}{4} \right )RT\)
4. \(\left ( \dfrac{13}{4} \right )RT\)
1. \(\left ( \dfrac{13}{2} \right )RT\)
2. \(\left ( \dfrac{11}{4} \right )RT\)
3. \(\left ( \dfrac{29}{4} \right )RT\)
4. \(\left ( \dfrac{13}{4} \right )RT\)
Subtopic: Law of Equipartition of Energy |
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At the same temperature, the root mean square (rms) speed of Neon \((\mathrm{Ne}),\) Chlorine \((\mathrm{Cl_2}),\) and oxygen hexafluoride \((\mathrm{OF_6})\) gases is measured. Which of the following correctly represents the order of their rms speeds?
1. \(\left(v_{\mathrm{rms}}\right)_{\mathrm{Ne}}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Cl}_2}<\left(v_{\mathrm{rms}}\right)_{\mathrm{OF}_6} \)
2. \(\left(v_{\mathrm {rms }}\right)_{\mathrm{Cl}_2}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Ne}}<\left(v_{\mathrm{rms}}\right)_{\mathrm{OF}_6} \)
3. \(\left(v_{\mathrm {rms }}\right)_{\mathrm{OF}_{\mathrm{6}}}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Cl}_2}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Ne}} \)
4. \(\left(v_{\mathrm{rms}}\right)_{\mathrm{OF}_6}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Ne}}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Cl}_2}\)
1. \(\left(v_{\mathrm{rms}}\right)_{\mathrm{Ne}}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Cl}_2}<\left(v_{\mathrm{rms}}\right)_{\mathrm{OF}_6} \)
2. \(\left(v_{\mathrm {rms }}\right)_{\mathrm{Cl}_2}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Ne}}<\left(v_{\mathrm{rms}}\right)_{\mathrm{OF}_6} \)
3. \(\left(v_{\mathrm {rms }}\right)_{\mathrm{OF}_{\mathrm{6}}}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Cl}_2}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Ne}} \)
4. \(\left(v_{\mathrm{rms}}\right)_{\mathrm{OF}_6}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Ne}}<\left(v_{\mathrm{rms}}\right)_{\mathrm{Cl}_2}\)
Subtopic: Types of Velocities |
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The ratio of density of oxygen (\(O_{8}^{16}\)) to the density of Helium(\(He_{2}^{4}\)) at STP is equal to:
1. 2
2. 4
3. 6
4. 8
1. 2
2. 4
3. 6
4. 8
Subtopic: Ideal Gas Equation |
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The ratio of temperature in \(\mathrm{K}\) of hydrogen and oxygen is \(2:1\). The ratio of their average kinetic energy per molecule is:
1. \(6:1\)
2. \(1:6\)
3. \(2:1\)
4. \(1: 2\)
1. \(6:1\)
2. \(1:6\)
3. \(2:1\)
4. \(1: 2\)
Subtopic: Kinetic Energy of an Ideal Gas |
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What is the molar-specific heat capacity of a diatomic gas in an isochoric process if it has an additional vibrational mode?
\(\begin{align} & {{1}{.}\;\frac{5}{2}{R}}\\ & {{2}{.}\;\frac{3}{2}{R}}\\ & {{3}{.}\;\frac{7}{2}{R}}\\ & {{4}{.}\;\frac{9}{2}{R}} \end{align} \)
\(\begin{align} & {{1}{.}\;\frac{5}{2}{R}}\\ & {{2}{.}\;\frac{3}{2}{R}}\\ & {{3}{.}\;\frac{7}{2}{R}}\\ & {{4}{.}\;\frac{9}{2}{R}} \end{align} \)
Subtopic: Law of Equipartition of Energy |
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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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