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Q.

The emissive power of a black body at $T = 300 K$ is $100 W a t t / m^{2}$ . Consider a body $B$ of area $A = 10 m^{}$ coefficient of reflection $r = 0.3$ and coefficient of transmission $t = 0.5$ . Its temperature is $400 K$ . Then which of the following is correct:

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a

The emissive power of $B$ is $63.2 W / m^{2}$

b

The emissive power of $B$ is $200 W / m^{2}$

c

The power emitted by $B$ is $80.4 W a t t$

d

The absorptivity of $B$ is $0.2$

answer is A, D.

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Detailed Solution

$a = 1 - r - t = 0.2 E m i s s i v e p o w e r o f a b l a c k b o d y a t 400 K = 100 \times {(\frac{400}{300})}^{4} W / m^{2} = \frac{100 \times 256}{81} W / m^{2} T h e r e f o r e e m i s s i v e p o w e r o f t h e b o d y B i s g i v e n b y E = e \times E_{b l a c k b o d y} = 0.2 \times (\frac{100 \times 256}{81}) W / m^{2} = 63.2 W / m^{2}$

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