Why do we need to equate the rate of energy of the second plate to zero?

[LCSphysicist]

Homework Statement

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Relevant Equations

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First i computed the rate of energy wrt time of the second plate:
$$dq_{2}/dt = A \sigma ((373)^4/2 + (273)^4/2 - T_{2}^4)$$
Equaliting it to zero we get the answer. But i am not sure why do we need to equality it to zero.
The q arrow on the figure suggest me that it is conservation of energy (radiation flux), but i don't get why.
The black body has transmission coefficient $\tau = 0$, so i don't understand why the flux of radiation need to be equal. The body could pretty well absorb the energy coming from 1 and emite an energy to 3 totally different, couldn't?

 

[hutchphd]

For thermal equilibrium, outgoing =ingoing. If that were not true, the temperature $T_2$ would change

 

[LCSphysicist]

For thermal equilibrium, outgoing =ingoing. If that were not true, the temperature $T_2$ would change

Yes i imagined it, but as the questions says nothing about equilibrium, i discarded the possibility. But since you pointed it too, i think that's enough to close this topic.