Assume we have an opaque body, irradiated from all sides with a spectral irradiance $E(\lambda)$ [W/m2]. Furthermore, we know its reflectance $R(\lambda)$. (It's in vacuum, and in no thermal contact to anything).

The heat absorbed per time will be $dQ_{irrad}/dt = (1-R(\lambda))*A*E(\lambda)$. Finally, we assume the situation has reached a steady state.

I would have assumed that in the steady state:

  • The body radiates a certain amount of heat per time $dQ_{rad}/dt$ and reaches a certian temperature $T$.

  • The same amount of power enters and leaves the body $dQ_{irrad}/dt = dQ_{rad}/dt$

I struggle, starting from this scenario:

  • to derive the temperature that the body will reach
  • to relate to the notion of (spectral) emissivity (how can I look at this to see $\epsilon(\lambda) = \alpha(\lambda)$)

Let me know if the problem if underspecified and even better how to solve it. Thank you for your help. Regards


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