# Black body radiation -- Spherical shell surrounding a star

Eitan Levy
Homework Statement:
A spherical shell with a radius of R surrounds a star with temperature T.

Find the amount of energy that the shell from the star in an hour.
Relevant Equations:
$$P=\sigma*A*T^4$$
I don't understand how this can be solved.

The official solution was:

$$F=\sigma*T^4$$

$$E=F*4\pi R^2*60*60$$

This doesn't make sense to me, as it seems to imply that the energy that the black body radiates depends on the radius of the shell. For a very large shell the body will reflect "infinity" energy.

Thank you.

Homework Helper
Gold Member
If a body emits a total of 100 Joules per second and you enclose it completely with a shell, 100 Joules per second will pass through the entire shell no matter how large the shell is.

Eitan Levy
Eitan Levy
If a body emits a total of 100 Joules per second and you enclose it completely with a shell, 100 Joules per second will pass through the entire shell no matter how large the shell is.

That's what I figured! Is the solution wrong?

Gordianus
You should previously know the star's radius.

hmmm27
Homework Helper
Gold Member
You should previously know the star's radius.
The radius R of the surrounding shell is given. That ought to be enough.

hmmm27
Homework Helper
2022 Award
But at equilibrium the temperature of the shell is not the temperature of the star. That is the point and the OP is correct.

Homework Helper
Gold Member
But at equilibrium the temperature of the shell is not the temperature of the star. That is the point and the OP is correct.
True, but there is no mention of equilibrium in the statement of the problem. My interpretation is that the shell is something like a Gaussian surface and not a material object.

Homework Helper
2022 Award
Gaussian surfaces do not radiate. The ##\sigma T^4## is for the surface that radiates and is emitted power per area. You are making the same mistake as the Prof I fear.

kuruman
Gordianus
Perhaps the homework has a wording problem. I think the sphere of radius R is a sort of Gaussian surface that encloses the star (that radiates to the 2.7 K background). Thus, we should know the star's radius (call it a)

hutchphd