Question

The power received at distance $d$ from a small metallic sphere of radius $r(<<d)$ and at absolute temperature $T$ is $P$. If the temperature is doubled and distance reduced to half of the initial value, then the power received at that point will be:

• A. $4p$
• B. $8p$
• C. $32p$
• D. $64p$

Answer 1

The correct option is D $64p$

Energy received per second i.e., power $P\alpha \frac{T^4}{d^2}=k\frac{T^4}{d^2}$

if temperature is double than T become 2T and distance become half than d become $\frac{d}{2}$

than power $p_1=k\frac{(2T{)}^4}{(\frac{d}{2}{)}^2}=64k\frac{T^4}{d^2}=64P$

Hence D option is correct.