Stefan's law for radiation between body and surroundings

[Remusco]

My PE handbook describes how to calculate the "Net Energy Exchange by Radiation Between Two Bodies", as shown below:

How can a single value of epsilon be used for heat transfer in both directions? Why does the body need to be small compared to the surroundings?

 

[pines-demon]

My PE handbook describes how to calculate the "Net Energy Exchange by Radiation Between Two Bodies", as shown below:

View attachment 354010



How can a single value of epsilon be used for heat transfer in both directions? Why does the body need to be small compared to the surroundings?

There is one $\varepsilon$ because the absorptivity of the body is the same as its emissivity per Kirchhoff's law of thermal radiation. You are calculating the heat on the body due to surroundings. If the surroundings are instead another body then you have to take into account the geometry of the second body.

Edit: not important, but who in their sane minds uses ft² and °R?