The coefficient of volume expansion of glycerine is $$49 \times 10^{-5} \mathrm{~K}^{-1}$$. The percentage change in its density for a $$50^{\circ} \mathrm{C}$$ rise in temperature is

The latent heat of vaporisation of water is $$2240 \mathrm{~J}$$. If the work done in the process of vaporisation of $$1 \mathrm{~g}$$ is $$168 \mathrm{~J}$$, the increase in internal energy is

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