Maharashtra Board Solutions for Chapter: Kinetic Theory of Gases and Radiation, Exercise 7: Exercises

Energy is emitted from a hole in an electric furnace at the rate of $20 \mathrm{W},$ when the temperature of the furnace is $727 °\mathrm{C}.$ What is the area of the hole? (Take Stefan's constant 6 to be $5.7\times {10}^{-8}{\text{Js}}^{-1}{\text{m}}^{-2}{\text{K}}^{-4}$
 

The emissive power of a sphere of area $0.02 {\mathrm{m}}^2$ is $0.5 \mathrm{kcal} {\mathrm{s}}^{-1} {\mathrm{m}}^{-2}$. What is the amount of heat radiated by the spherical surface in $20 \mathrm{s}$? 
 

Compare the rates of emission of heat by a blackbody maintained at $727 °\mathrm{C}$ and at $227 °\mathrm{C}$, if the blackbodies are surrounded by an enclosure (black) at $27 °\mathrm{C}$. What would be the ratio of their rates of loss of heat ? 
 

Earth's mean temperature can be assumed to be $280 \mathrm{K}$. How will the curve of blackbody radiation look like for this temperature? Find out ${\mathrm{\lambda }}_{max}$. In which part of the electromagnetic spectrum, does this value lie? (Take Wien's constant $\mathrm{b}=2.897\times {10}^{-3}\mathrm{mK}$
 

A small-blackened solid copper sphere of radius $2.5 \mathrm{cm}$ is placed in an evacuated chamber. The temperature of the chamber is maintained at $100 °\mathrm{C}$. At what rate energy must be supplied to the copper sphere to maintain its temperature at $110 °\mathrm{C}$? (Take Stefan's constant a to be $5.670\times {10}^{-8}{\mathrm{Js}}^{-1}{\mathrm{m}}^{-2}{\mathrm{K}}^{-4},\mathrm{\pi }=3.1416$ and treat the sphere as a blackbody.) 
 

Find the temperature of a blackbody if its spectrum has a peak at

${\mathrm{\lambda }}_{max}=700$ nm (visible)

Wien's constant $\mathrm{b}=2.897\times {10}^{-3}\mathrm{mK}$

Find the temperature of a blackbody if its spectrum has a peak at

 ${\mathrm{\lambda }}_{max}=3\mathrm{cm}$ (microwave region) 

Wien's constant $\mathrm{b}=2.897\times {10}^{-3}\mathrm{mK}$

Find the temperature of a blackbody if its spectrum has a peak at

 ${\mathrm{\lambda }}_{max}=3\mathrm{m}$ (short radio waves). Take Wien's constant $\text{b}=2.897\times {10}^{-3}\text{mK}$