A black body at temperature $$127^{\circ} \mathrm{C}$$ radiates heat at the rate of $$5 \mathrm{~cal} / \mathrm{cm}^2 \mathrm{~s}$$. At a temperature $$927^{\circ} \mathrm{C}$$, its rate of emission in units of $$\mathrm{cal} / \mathrm{cm}^2 \mathrm{~s}$$ will be

A Carnot engine has the same efficiency between (i) $$100 \mathrm{~K}$$ and $$600 \mathrm{~K}$$ and (ii) $$\mathrm{T} \mathrm{K}$$ and $$960 \mathrm{~K}$$. The temperature $$\mathrm{T}$$ in kelvin of the sink is

For an ideal gas the density of the gas is $$\rho_0$$ when temperature and pressure of the gas are $$T_0$$ and $$P_0$$ respectively. When the temperature of the gas is $$2 \mathrm{~T}_0$$, its pressure will be $$3 \mathrm{P}_0$$. The new density will be

The temperature gradient in a rod of length $$75 \mathrm{~cm}$$ is $$40^{\circ} \mathrm{C} / \mathrm{m}$$. If the temperature of cooler end of the rod is $$10^{\circ} \mathrm{C}$$, then the temperature of hotter end is