Considering an antenna placed inside a blackbody enclosure at temperature T, the power received per unit bandwidth is:

\(latex \omega = kT\)

where k is Boltzmann constant.

This relationship derives from considering a constant brightness \(latex B\) in all directions, therefore Rayleigh Jeans law tells:

\(latex B = \dfrac{2kT}{\lambda^2}\)

Power per unit bandwidth is obtained by integrating brightness over antenna beam

$latex = A_e B ( , ) P_n ( , ) d $

therefore

$latex = A_e_A $

where:

- \(latex A_e\) is antenna effective aperture
- \(latex \Omega_A\) is antenna beam area

$latex ^2 = A_e_A $ another post should talk about this

finally:

$latex = kT $

which is the same noise power of a resistor.

source : Kraus Radio Astronomy pag 107