# Heat transfer by radiation between two plates

#### Karol

1. Homework Statement
Two large plates are parallel and close to each other, vacuum is between them. they are held at 2000K and 3000K.
What is the energy transfer rate between them.

2. Homework Equations
The energy emission rate per unit area-the Stefan-Boltzmann Law: $$R=\varepsilon\sigma T^4$$
$\varepsilon$ is the emissivity of the surface
$\sigma=5.672E-8[w/sec]$

3. The Attempt at a Solution
The solution is 368[w/m2], it's the answer if the emission is of a black body:
$1\cdot 5.672E-8\cdot\left(300^4-200^4\right)=368$
But why don't the emissivities of the surfaces count? what if one surface emits more or less than the other?
In the Stefan-Boltzman formula the outer temperature exists, not the nature of the surrounding surfaces.
I guess it has something to do with the fact that the rest of the radiation, which isn't absorbed, is reflected and comes into account

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#### mfb

Mentor
But why don't the emissivities of the surfaces count?
They do count, and the problem statement should specify that ideal black bodies are meant. The sign of the energy transfer cannot change, but the overall magnitude of exchanged energy can go down.

#### Karol

The sign of the energy transfer cannot change, but the overall magnitude of exchanged energy can go down.
What do you mean by "sign"?

#### haruspex

Homework Helper
Gold Member
2018 Award
What do you mean by "sign"?
Meaning which way the net flow goes.
If one body has lower emissivity than that of a black body then it both emits less and absorbs less. Different emissivities cannot result in the net flow being from the cooler to the hotter.

#### Karol

Of course not from the cooler to the hotter, but different emissivities must mean smaller energy flow. it doesn't matter which plate's emissivity is smaller, right?

#### haruspex

Homework Helper
Gold Member
2018 Award
Of course not from the cooler to the hotter
You say 'of course', but if the emissivity affected only the emission rate and not the absorption rate then you could have the paradoxical situation that a hot body with low emissivity could gain energy from a cooler body.
but different emissivities must mean smaller energy flow. it doesn't matter which plate's emissivity is smaller, right?
It's not that they're different, just that one, the other or both are lower than a black body's.

Thanks

#### Karol

Why in an insulated chamber the emission of a body and the emission of the walls is black body? why don't we take into account the emissivity of the walls?

#### mfb

Mentor
Why in an insulated chamber the emission of a body and the emission of the walls is black body?
It is not.
The energy density in the cavity does not depend on the emissivity, but the energy exchange rate with the objects does.

#### Karol

The energy density in the cavity does not depend on the emissivity
Why? if the walls inside emit low radiation, because of small emissivity, then the energy density in the opening will also be low, no?

#### haruspex

Homework Helper
Gold Member
2018 Award
Why? if the walls inside emit low radiation, because of small emissivity, then the energy density in the opening will also be low, no?
No. This is exactly the same point as for the two bodies at different temperatures. If the emissivity is low then the absorption from the cavity is correspondingly low. Equilibrium will still be achieved when the energy density corresponds to the temperature of the enclosure.

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