The earth receives solar energy at the rate of $2 \mathrm{cal} {\mathrm{cm}}^2$ per min. Assuming the  radiation to be black body in character, estimate the surface temperature of the sun. Given that $s=5.67\times {10}^{-8} \mathrm{W}/{\mathrm{m}}^2/{\mathrm{K}}^4$ and angular diameter of the sun $=32$ min of arc.

The only possibility of heat flow in a thermos flask is through its cork which is $75{ \mathrm{cm}}^2$ in area and $5 \mathrm{cm}$ thick. Its thermal conductivity is $0.0075 \mathrm{cal}/\mathrm{cm}-\sec -{}^{\circ }\mathrm{C}$. The outside temperature is $40°\mathrm{C}$ and latent heat of ice is $80 \mathrm{cal}-{\mathrm{g}}^{-1}$. Find the time taken by $500 \mathrm{g}$ of ice at $0°\mathrm{C}$ in the flask to melt into water at $0{}^{\circ }\mathrm{C}$.

A brass boiler has a base area of $0.15 {\mathrm{m}}^2$ and thickness of $1.0 \mathrm{cm}$. It boils water at the rate of $6.0 \mathrm{kg}/\min$ when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass is $109 {\mathrm{Js}}^{-1}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$; Heat of vaporisation of water is $2256\times {10}^3 {\mathrm{Jkg}}^{-1}$.

Two rods $A$ and $B$ of same length and cross-sectional area are connected in series and a temperature difference of $100 °\mathrm{C}$ is maintained across the combination as shown in the given figure. If the thermal conductivity of the rod $A$ is $3k$ and that of rod $B$ is $k$, then plot the variation of temperature along the length of the rod.