Question

A spherical ball $A$ of surface area $10{\text{cm}}^2$ is kept at the centre of a hollow spherical shell of area $20{\text{cm}}^2$. Surface of $A$ and inner surface of $B$ behave as black bodies. Both $A$ and $B$ are at $300\text{K}$. Find the radiation energy emitted per second by the inner surface of $B$.

• A. $0.92\text{W}$
• B. $1.84\text{W}$
• C. $9.2\text{W}$
• D. $4.1\text{W}$

Answer 1

The correct option is A $0.92\text{W}$


Given that, $(\text{Area}{)}_B=2(\text{Area}{)}_A$
Outer surface of $\text{A}$ and inner surface of $\text{B}$ are black bodies. [i.e $a=1,e=1$]

Radiation emitted by body $A$
${\left(\frac{dQ}{dt}\right)}_A=e\sigma A{T}_A^4$
$=1\times (5.67\times {10}^{-8})\times (10\times {10}^{-4})\times (300{)}^4\text{J/s}$
$=0.46\text{W}$

We know that, Radiant power of $B$ is given by,
${\left(\frac{dQ}{dt}\right)}_B=e\sigma A_0\left(T^4\right)$
$\because A_B=2A_A$ and both the spheres are at the same temperature, we can say that,
${\left(\frac{dQ}{dt}\right)}_B=2{\left(\frac{dQ}{dt}\right)}_A$
$\Rightarrow {\left(\frac{dQ}{dt}\right)}_B=2\left(0.46\right)=0.92\text{W}$