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 mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
1. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}^2} \)
2. \( \frac{1}{\sqrt{2} n^2 \pi \mathrm{d}^2} \)
3. \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2} \)
4. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)

The graph between volume and temperature in Charle's law is?
1. an ellipse
2. a circle
3. a straight line
4. a parabola

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:

What is the average thermal energy of a helium atom at room temperature (\(27^{\circ}\mathrm{C}\))?

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. $\mathit{5}nRT$
4. $\frac{7}{2}nRT$

Two isotherms are drawn at temperatures ${\mathrm{T}}_1$ $\mathrm{and}$ ${\mathrm{T}}_2$ as shown. The ratio of mean speed  at ${\mathrm{T}}_1$ $\mathrm{and}$ ${\mathrm{T}}_2$ is:
  

The translational kinetic energy of oxygen molecules at room temperature is 60 J. Their rotational kinetic energy will be?

1. 40 J

2. 60 J

3. 50 J

4. 20 J