A cubical box of side $$2 \mathrm{~m}$$ contains helium gas. It was observed that in a time of 1 second, an atom travelling with the root-mean-square speed parallel to one of the edges of the cube, made 250 hits with one of the walls, without any collision with other atoms. The average kinetic energy of the helium gas is Take $$R=\frac{25}{3} \mathrm{~J} / \mathrm{mol}-\mathrm{K}$$ and $$\mathrm{kB}=1.38 \times 10^{-23} \mathrm{JK}{ }^{-1}$$

A glass of hot water cools from $$90^{\circ} \mathrm{C}$$ to $$70^{\circ} \mathrm{C}$$ in 3 minutes when the temperature of surroundings is $$20^{\circ} \mathrm{C}$$. What is the time taken by the glass of hot water to cool from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$ if the surrounding temperature remains the same at $$20^{\circ} \mathrm{C}$$ ?

A cubical box of side $$1 \mathrm{~m}$$ contains Boron gas at a pressure of $$100 \mathrm{~Nm}^{-2}$$. During an observation time of 1 second, an atom travelling with the rms speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. The total mass of gas in the box in gram is

A one $\mathrm{kg}$ block of ice at $$-1.5^{\circ} \mathrm{C}$$ falls from a height of $$1.5 \mathrm{~km}$$ and is found melting. The amount of ice melted due to fall, if $$60 \%$$ energy is converted into heat is (Specific heat capacity of ice is $$0.5 \mathrm{~cal} \mathrm{~g}^{-1} \mathrm{~C}^{-1}$$, Latent heat of fusion of ice $$=80 \mathrm{~cal~g}^{-1}$$ )