Interaction between blackbodies in relation to the second law

[Shunyata]

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?

 

[cjl]

Sure it can. In fact, it always will be. However, B1 will always be giving more energy to B2 than the reciprocal effect, so the net energy exchange will always involve B1 giving energy to B2.

 

[Shunyata]

Is it as simple as

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?