Radiation to a small object from surroundings

[Dong Aleta]

In the energy balance of a system where a small object at T₁ enclosed in a body at T₂ given by the Stefan-Boltzmann equation

q = A₁ε₁σT₁⁴ - A₁α₁₂σT₂⁴

shouldn't it be a differential equation since the small body could be absorbing/releasing sufficient net energy from the enclosing body that will change its temperature, thereby changing its rate of heat transfer through radiation? I guess the same could also be said for the enclosing body.

 

[Drakkith]

I assume that the equation is used strictly to find the energy balance at a single time, not to find the energy balance over timescales long enough where the temperature of either object could change.

 

[Dong Aleta]

I assume that the equation is used strictly to find the energy balance at a single time, not to find the energy balance over timescales long enough where the temperature of either object could change.

I thought so too, but I had to check. I imagined there to be a differential form of this. But anyway, thanks for the response!

 

[Drakkith]

I thought so too, but I had to check. I imagined there to be a differential form of this. But anyway, thanks for the response!

There may be. I'm not certain to be honest.