Question

A spherical body of area A and emissivity $e=0.6$ is kept inside a perfectly black body. Total heat radiated by the body at temperature $T$

• A. $0.8e\sigma A{T}^4$
• B. $0.4e\sigma A{T}^4$
• C. $0.6e\sigma A{T}^4$
• D. $1.0e\sigma A{T}^4$

Answer 1

The correct option is D $1.0e\sigma A{T}^4$

According to Stefan's Boltzman law, the thermal energy radiated by a black body radiator per second per unit area is proportional to fourth power of the absolute temperature and is given by

$\frac{P}{A}=\sigma T^4$ ..............(1)

For the hot bodies other than black body radiator equation (1) becomes,

$\frac{P}{A}=e\sigma T^4$

$P=e\sigma A{T}^4$ .................(2)

where, $e$ is the emissivity of the body.

Now, when such hot body is kept inside a perfectly black body, the total thermal radiation is the sum of emitted radiations (in open) and the part of incident radiations reflected from the walls of the perfectly black body. This will give black body radiations, hence the total radiations emitted by the body will be,

$P=1.0e\sigma A{T}^4$.