The intensity of solar radiation just outside the earth's atmosphere is measured to be $1.4 \mathrm{kW}/{\mathrm{m}}^2$. If the radius of the sun $7\times {10}^8 \mathrm{m}$, while the earth-sun distance is $150\times {10}^6 \mathrm{km}$, then find

the intensity of solar radiation at the surface of the sun,

The intensity of solar radiation just outside the earth's atmosphere is measured to be $1.4 \mathrm{kW}/{\mathrm{m}}^2$. If the radius of the sun $7\times {10}^8 \mathrm{m}$, while the earth-sun distance is $150\times {10}^6 \mathrm{km}$, then find

the temperature at the surface of the sun assuming it to be a black body,

The intensity of solar radiation just outside the earth's atmosphere is measured to be $1.4 \mathrm{kW}/{\mathrm{m}}^2$. If the radius of the sun $7\times {10}^8 \mathrm{m}$, while the earth-sun distance is $150\times {10}^6 \mathrm{km}$, then find

the most probable wavelength in solar radiation.

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 $2256\times {10}^3 {\mathrm{Jkg}}^{-1}$.