Question

A surface at temperature $T_o$ $K$ receives power $P$ by radiation from a small sphere at temperature $T<T_o$ and at a distance $d$. If both $T$ and $d$ are doubled, the power received by the surface will become

• A. $P$
• B. $2P$
• C. $4P$
• D. $16P$

Answer 1

The correct option is C $4P$

The power with which the source radiates:

• Directly proportional the fourth power of absolute temperature
• Inversely proportional to the square of distance from the source

i.e.
$P\propto T^4$
$P\propto \frac{1}{d^2}$
$P=k\frac{T^4}{d^2}$
When both temperature and distance from source is doubled.
$P_2=k\frac{(2T{)}^4}{(2d{)}^2}=k\frac{4T^4}{d^2}=4P$