Question

The emissive power of a black body at $T=300\text{K}$ is $100{\text{W/m}}^2$. Consider a body $B$ of area $A=10{\text{m}}^2$, coefficient of reflectivity $r=0.3$ and coefficient of transmission $t=0.5$. Its temperature is $300\text{K}$. Then choose the correct statement.

• A. The emissive power of $B$ is $20{\text{W/m}}^2$.
• B. The emissive power of $B$ is $200{\text{W/m}}^2$.
• C. The power emitted by $B$ is $100\text{W}$.
• D. The emissivity of $B$ is $0.2$.

Answer 1

Answer: (A), (D)

The correct options are
A The emissive power of $B$ is $20{\text{W/m}}^2$.
D The emissivity of $B$ is $0.2$.

We know that,
$a+r+t=1$
$\Rightarrow a=1-r-t$
$\Rightarrow a=[1-0.3-0.5]=0.2$

Applying Kirchhoff's law,
emissivity$\left(e\right)=\text{absorptive power}\left(a\right)$
$\Rightarrow e=0.2$
Emissive power of body $B$,
$E=\left(100\right)\left(0.2\right)=20{\text{W/m}}^2$
$\text{Power emitted}=\text{Emissive Power}\times \text{Area}$
$=20\times 10=200\text{W}$
Thus, option (a) and (d) are correct.