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.	\(2\times10^{6}\)

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

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. $\frac{{\mathrm{P}}_0}{2}$

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

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. \( \dfrac{1}{\sqrt{2} n \pi {d}}\)

If the pressure of a gas is doubled, then the average kinetic energy per unit volume of the gas will be:

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. \(20~\text J\)

When the gas in an open container is heated, the mean free path:
1. Increases
2. Decreases
3. Remains the same
4. Any of the above depending on the molar mass

The change in the internal energy of an ideal gas does not depend on?