If $$\mathrm{n}$$ is the number density and $$\mathrm{d}$$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

The heat absorbed by a system in going through the given cyclic process is :

If the collision frequency of hydrogen molecules in a closed chamber at $$27^{\circ} \mathrm{C}$$ is $$\mathrm{Z}$$, then the collision frequency of the same system at $$127^{\circ} \mathrm{C}$$ is :

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $$\gamma=3 / 2$$. The work done by the gas in the process is:

$$(\mu=1 \text { mole })$$