# Interaction between blackbodies in relation to the second law

I am trying to understand the behavior of blackbodies in interaction with each other.

Conditions as follows.

$1)$ There are two blackbodies, say $B_1$ and $B_2$, with corresponding temperature $T_1$ and $T_2$.

$2)$ Initially $T_1>T_2$.

$3)$ $B_1$ and $B_2$ have thermal contact only through radiation exchange.

And finally my question,

Can $B_2$ give energy to $B_1$ or is this prevented by the second law?

$dQ\Big( \frac{1}{T_2} - \frac{1}{T_1}\Big)=dQ\Big( \frac{T_1-T_2}{T_1T_2}\Big)>0,$
if $dQ=dQ_1 - dQ_2$ is the net-heat where positive direction is from $B_1$ to $B_2$ and $dQ_1>dQ_2$?