Thermal and Thermodynamic Equilibrium

Thermal radiation is radiation emitted by matter in thermal equilibrium. There is a great deal of confusion when discussing thermal equilibrium since it is often used as a synonym for thermodynamic equilibrium. However, these two concepts are different although related. A body in thermodynamic equilibrium has reached thermal equilibrium as well as mechanical, chemical, and radiative equilibrium. This means that two bodies in thermodynamic equilibrium need to have achieved the same temperature, pressure, and chemical potential and there must be a zero net flux of radiation. The radiative equilibrium condition can be expressed as:

(1)   \begin{equation*}h = \int_0^\infty h_\nu d\nu = 0\end{equation*}

where h_\nu is equal to the negative monochromatic gradient of the flux:

(2)   \begin{equation*}h_\nu = -\grad F_\nu\end{equation*}

Thermal equilibrium was instead defined according to the Zeroth law of thermodynamics.

Which variable is defined by the Zeroth law of thermodynamics?

To be continued…