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. \( \dfrac{1}{\sqrt{2} n \pi {d}}\)

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

A gas at pressure ${\mathrm{P}}_0$ is contained in a vessel. If the masses of all the molecules are halved and their speeds doubled, the resulting pressure would be:

1. $4{\mathrm{P}}_0$

2. $2{\mathrm{P}}_0$

3. ${\mathrm{P}}_0$

4. $\frac{{\mathrm{P}}_0}{2}$

The rms speed of the molecules of an enclosed gas is \(v\). What will be the rms speed if the pressure is doubled, keeping the temperature constant?

Two closed containers of equal volume are filled with air at pressure ${\mathrm{P}}_0$ and temperature ${\mathrm{T}}_0$. Both are connected by a narrow tube. If one of the containers is maintained at temperature ${\mathrm{T}}_0$ and the other at temperature T, then new pressure in the container will be:

1. $\frac{2{\mathrm{P}}_0\mathrm{T}}{\mathrm{T}+{\mathrm{T}}_0}$

2. $\frac{{\mathrm{P}}_0\mathrm{T}}{\mathrm{T}+{\mathrm{T}}_0}$

3. $\frac{{\mathrm{P}}_0\mathrm{T}}{2(\mathrm{T}+{\mathrm{T}}_0)}$

4. $\frac{\mathrm{T}+{\mathrm{T}}_0}{{\mathrm{P}}_0}$

The ratio of the average translatory kinetic energy of \(\mathrm{He}\) gas molecules to ${\mathrm{}}_{}$\(\mathrm{O_2}\) gas molecules at the given temperature is:
1. \(\frac{25}{21}\)
2. \(\frac{21}{25}\)
3. \(\frac{3}{2}\)
4. \(1\)

Without change in temperature, a gas is forced in a smaller volume. Its pressure increases because its molecules:

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:

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