Q. No.What is the graph between volume and temperature in Charle's law?
1. An ellipse
2. A circle
3. A straight line
4. A parabola
1. An ellipse
2. A circle
3. A straight line
4. A parabola
(\(k_B\) is Boltzmann constant and \(T\) absolute temperature)
| 1. | \(\dfrac{3}{2}k_BT\) | 2. | \(\dfrac{5}{2}k_BT\) |
| 3. | \(\dfrac{7}{2}k_BT\) | 4. | \(\dfrac{1}{2}k_BT\) |
The mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
1. \( \dfrac{1}{\sqrt{2} n \pi {d}^2} \)
2. \( \dfrac{1}{\sqrt{2} n^2 \pi {d}^2} \)
3. \(\dfrac{1}{\sqrt{2} n^2 \pi^2 d^2} \)
4. \( \dfrac{1}{\sqrt{2} n \pi {d}}\)
Without change in temperature, a gas is forced in a smaller volume. Its pressure increases because its molecules:
| 1. | strike the unit area of the container wall more often. |
| 2. | strike the unit area of the container wall at a higher speed. |
| 3. | strike the unit area of the container wall with greater force. |
| 4. | have more energy. |
If at a pressure of \(10^6\) dyne/cm2, one gram of nitrogen occupies \(2\times10^4\) c.c. volume, then the average energy of a nitrogen molecule in erg is:
| 1. | \(14\times10^{-13}\) | 2. | \(10\times10^{-12}\) |
| 3. | \(10^{6}\) | 4. | \(2\times10^{6}\) |
When a large bubble rises from the bottom of a lake to the surface, its radius doubles. The atmospheric pressure is equal to that of a column of water of height H. The depth of the lake is:
1. H
2. 2H
3. 7H
4. 8H
Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. The equation in kinetic theory \(PV = \dfrac{2}{3}E,\) \(E\) is:
| 1. | the total energy per unit volume. |
| 2. | only the translational part of energy because rotational energy is very small compared to translational energy. |
| 3. | only the translational part of the energy because during collisions with the wall, pressure relates to change in linear momentum. |
| 4. | the translational part of the energy because rotational energies of molecules can be of either sign and its average over all the molecules is zero. |
| 1. | \(3:1\) | 2. | \(9:1\) |
| 3. | \(1:1\) | 4. | \(1:4\) |
Which of the following graphs, shows the variation of the mean kinetic energy \(E\) of an ideal gas molecule with temperature
| 1. |  |
2. |  |
| 3. |  |
4. |  |
The translational kinetic energy of \(n\) moles of a diatomic gas at absolute temperature \(T\) is given by:
1. \(\frac{5}{2}nRT\)
2. \(\frac{3}{2}nRT\)
3. \(5nRT\)
4. \(\frac{7}{2}nRT\)
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