Q. No.An increase in the temperature of a gas-filled in a container would lead to:
1.
decrease in the intermolecular distance.
2.
increase in its mass.
3.
increase in its kinetic energy.
4.
decrease in its pressure.
To find out the degree of freedom, the correct expression is:
1. \(f=\frac{2}{\gamma -1}\)
2. \(f=\frac{\gamma+1}{2}\)
3. \(f=\frac{2}{\gamma +1}\)
4. \(f=\frac{1}{\gamma +1}\)
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. |
The ratio of the average translatory kinetic energy of \(\mathrm{He}\) gas molecules to \(\mathrm{O_2}\)
1. \(\frac{25}{21}\)
2. \(\frac{21}{25}\)
3. \(\frac{3}{2}\)
4. \(1\)
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
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. | \(2\times10^{6}\) |
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. \(\frac{7}{2}nRT\)
The translational kinetic energy of oxygen molecules at room temperature is \(60~\text J.\) Their rotational kinetic energy will be?
1. \(40~\text J\)
2. \(60~\text J\)
3. \(50~\text J\)
4. \(20~\text J\)
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