A spherical body of area and emissivity is kept inside a perfectly black body. Total heat radiated by the body at temperature [2005]

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 $T$ [2005]

Smart Achievers · Accepted Answer

(4)

$By Stefan's law$

For black body, $\frac{P}{A} = σ T^{4}$

For hot bodies other than black body, $\frac{P}{A} = e σ A T^{4}$

Now, when such hot body is kept inside a perfectly black body, the total thermal radiation is 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 radiation emitted by the body will be $P = 1.0 e σ A T^{4}$ .

Solution

Q.
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 $T$ [2005]

1 $0.4 A T^{4}$

2 $0.8 A T^{4}$

3 $0.6 A T^{4}$

4 $1.0 A T^{4}$

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Solution

Q. 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 [2005]

1 0.4AT4

2 0.8AT4

3 0.6AT4