The mean free path of a molecule of diameter $5 \times 10^{-10}$ m at the temperature $41^{\circ}$C and pressure $1.38 \times 10^5$ Pa, is given as ________ m. (Given $k_B = 1.38 \times 10^{-23}$ J/K).

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^{\circ} \mathrm{C}$ to $120^{\circ} \mathrm{C}$?

10 kg of ice at $-10^{\circ} \mathrm{C}$ is added to 100 kg of water to lower its temperature from 25 ${ }^{\circ} \mathrm{C}$. Consider no heat exchange to surroundings. The decrement to the temperature of water is $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$.

(specific heat of ice $=2100 \mathrm{~J} / \mathrm{Kg} .{ }^{\circ} \mathrm{C}$, specific heat of water $=4200 \mathrm{~J} / \mathrm{Kg} .{ }^{\circ} \mathrm{C}$, latent heat of fusion of ice $=3.36 \times 10^5 \mathrm{~J} / \mathrm{Kg}$ )

In the following $p-V$ diagram the equation of state along the curved path is given by $(V-2)^2=4 a p$ where $a$ is a constant. The total work done in the closed path is