How efficiency works for objects

Question

Imagine, there is an object(objA) which is not a black body. But this object is a kind of object that does not reflect any energy(light). It can only absorb and transmit.

We know that blackbody emits radiation at the perfect efficiency at different wavelengths.

Now imagine light hits the objA which then transmits this light(hence lets call this reemitting). In this case, why would not this objA have the perfect efficiency at different wavelengths? You might say that objA might absorb some of the light but this absorbed one will cause new re-emit and the transmitted light + re-emitted should still be equal to the efficiency of black body.

Could you explain why not ?

Answer 1

As for me what you described is same back-body, only shielded with some coating outside which doesn't pass radiation outwards. Keep in mind, that black body doesn't have any radiating direction limitations. So part of black body radiation goes inside back to black body as well. So this blackbody emitted radiation going inwards,- you named "transmitted" radiation. So yes, for this type of backwards radiation same black body radiation effectivity law applies.

Closest analog to such construct is black holes, which absorb every type of radiation and (almost) emit none, except for gravitational waves (but for these black-body law does not apply, because it's just space-time curvature and not EM waves). Also there is a Hawking radiation. For this type radiation of black hole,- indeed black-body radiation law applies. For example, black hole with mass $1~M_☉$ according to Wien displacement law, $$ \lambda _{\text{peak}}={\frac {b}{T}} = \frac {2.90~mK \cdot m}{60~nK} \approx 48~km \tag 1 ,$$

will emit Hawking EM radiation with $48~km$ of wavelength. Part of this radiation is absorbed back by a black hole, i.e. goes back to interior of event horizon, but other part - escapes black hole once and for all. So it's not "a perfect non-emitter" as you search for, but at least it's closest construct so far in the universe.

Answer 2

Black body re-emits all the energy that it absorbs and is in equilibrium with its environment. Any other object that re-emits all the energy that it absorbs is not in equilibrium, i.e., it has entropy lower than the black body and will gradually evolve towards having a black body spectrum... unless it has internal energy sources, which would keep it permanently out of equilibrium (perhaps eventually reaching some kind of a steady-state.)

See also Aren't all objects luminous in a sense?