First slide
Radiation
Question

A Black metal foil receives radiation of  power P from a hot  sphere at absolute temperature T, kept at a distance d. If the temperature is doubled and distance is halved, then Power will be

Easy
Solution

Power radiated from the surface of a hot spherical surface is P = eσAT4, Intensity \large I=\frac {P}{4\pi d^2}
\large \therefore I\propto T^4/d^2
\large T_1=T,\;T_2=2T;\;d_1=d,\;d_2=d/2,\;P_1=P
\large P\propto \frac {T^4}{d^2};\;\frac {P_1}{P_2}=\left ( \frac {T_2}{T_1} \right )^4\left ( \frac {d_2}{d_1} \right )^2=\frac {1}{16}\left ( \frac {1}{4} \right )
\large P_2=64P

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