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 $$20^{\circ} \mathrm{C}$$ ? ($$R=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$)

An iron piece of mass $$200 \mathrm{~g}$$ is kept inside a furnace for some time and then put in a calorimeter of water equivalent $$20 \mathrm{~g}$$ containing $$230 \mathrm{~g}$$ of water at $$20 \mathrm{C}$$. The steady state temperature attained by the mixture is $$60^{\circ}$$. The temperature of the furnace is (Specific heat capacity of iron is $$470 \mathrm{~J~kg}^{-1} \mathrm{C}^{-1}$$ )

An ideal gas changes its state from $$\mathrm{A}$$ to $$\mathrm{C}$$ in two different paths $$\mathrm{ABC}$$ and $$\mathrm{AC}$$. The internal energy of the gas at state $$\mathrm{C}$$ is $$20 \mathrm{~J}$$ and at state $$\mathrm{B}$$ is $$10 \mathrm{~J}$$. Heat supplied to the gas to go from $$\mathrm{B} \rightarrow \mathrm{C}$$ is