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 $$=80 \mathrm{~cal~g}^{-1}$$ )

An electric bulb of volume $$300 \mathrm{~cm}^3$$ was sealed off during manufacture at a pressure of $$1 \mathrm{~mm}$$ of mercury at $$27{ }^{\circ} \mathrm{C}$$. The number of air molecules contained in the bulb is, $$(\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$ and $$N_A=6.02 \times 10^{23})$$