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. $f=\frac{1}{\gamma +1}$

An increase in the temperature of a gas-filled in a container would lead to:

Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory, \(PV = \frac{2}{3}E\)$,$ \(E\) is:

The ratio of the average translatory kinetic energy of He gas molecules to ${\mathrm{O}}_2$ gas molecules is:

1. $\frac{25}{21}$

2. $\frac{21}{25}$

3. $\frac{3}{2}$

4. 1

The graph between volume and temperature in Charle's law is?
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. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}^2} \)
2. \( \frac{1}{\sqrt{2} n^2 \pi \mathrm{d}^2} \)
3. \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2} \)
4. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)

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:

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. $\frac{7}{2}nRT$

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