The maximum wavelength of radiations emitted at $900 \mathrm{K}$ is $4 \mathrm{\mu m}$. What will be the maximum wavelength of radiations emitted at $1200 \mathrm{K}?$

The effective temperature of the source is approximately (Wien's displacement constant, $b=2.89\times {10}^{-3} \mathrm{m} \mathrm{K}$

The sun rays are allowed to fall on a lens of diameter $20 \mathrm{cm}$. They are then brought to focus on a calorimeter containing $20 \mathrm{g}$ of ice. If the absorption by the lens is negligible, the time required to melt all the ice is

(Solar constant $=1.9 \mathrm{cal} {\min }^{-1} {\mathrm{cm}}^{-2}$ and $L=80 \mathrm{cal} {\mathrm{g}}^{-1}$)