A conducting rod of length $$1 \mathrm{~m}$$ has area of cross-section $$10^{-3} \mathrm{~m}^2$$. One end is immersed in baiting water $$\left(100^{\circ} \mathrm{C}\right)$$ and the other end in Ice $$\left(0^{\circ} \mathrm{C}\right)$$. If coefficient of thermal conductivity of $$\mathrm{rod}$$ is $$96 \mathrm{~cal} / \mathrm{sm}^{\circ} \mathrm{C}$$ and latent heat for ice is $$8 \times 10^{-4} \mathrm{cal} / \mathrm{kg}$$ then the amount of ice which will melt in one minute is

Two stars 'P' and 'Q' emit yellow and blue light respectively. The relation between their temperatures $$\left(\mathrm{T}_{\mathrm{P}}\right.$$ and $$\left.\mathrm{T}_{\mathrm{Q}}\right)$$ is

A perfectly black body emits a radiation at temperature 'T$$_1$$' K. If it is to radiate at 16 times this power, its temperature 'T$$_2$$' K should be

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $$T \propto {1 \over {\sqrt V }}$$. The value of $$\gamma$$ for the gas is ($$\gamma = {{{C_p}} \over {{C_v}}},V = $$ Volume of the gas)