Question

A copper sphere is suspended in an evacuated chamber maintained at 300 K. The sphere is maintained at a constant temperature of 500 K by heating it electrically. A total of 210 W of electric power is needed to do it. When the surface of the copper sphere is completely blackened, 700 W is needed to maintain the same temperature of the sphere. Calculate the emissivity of copper.

• A. 0.5
• B. 0.4
• C. 0.3
• D. 0.2

Answer 1

The correct option is C

0.3

Before painting it black the power needed = $e\sigma A(T^4-T_0^4)=210$ ...(i)

T = 500 K

$T_0$ = 300 K

e $\to$ emissivity

After the paint the surface behaves like a black body.

$\therefore \sigma A(T^4-T_0^4)=700$ ...(ii)

Dividing (i) and (ii)

$e=\frac{210}{700}$

$\Rightarrow$ e = 0.3