Internal energy of $$\mathrm{n}_1$$ moles of hydrogen at temperature T is equal to internal energy of $$\mathrm{m}_2$$ moles of helium at temperature 2T. The ratio $$\frac{n_1}{n_2}$$ is

A cylinder of fixed capacity 44.81 contains hydrogen gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $$20^{\circ} \mathrm{C}$$ ? ($$R=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$)

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