# Would a hypothetical perfect reflector emit thermal radiation?

The question says it all. I believe a hypothetical perfect reflector is what's referred to as a "white body", but I might be wrong. From what I understand such a hypothetical perfect reflector should still emit thermal radiation based on its own temperature (as long as it's above 0 K, of course), just not absorb any thermal radiation from the environment. Is that not the case? The reason I ask is because I can't find a clear answer to it anywhere, and I only find texts and graphics suggesting that such a body wouldn't emit any thermal radiation at all, which does not sound right.

• My guess is that if it emits radiation, then it will quickly reach T=0, it should not be difficult to calculate how long this would take. Commented Mar 9 at 20:20
• I'd hazard a guess that this is the reason why perfect reflectors don't exist. If the material admits different energy levels and transitions between them, then it can emit and absorb corresponding thermal radiation. But then it's not a perfect reflector. Commented Mar 9 at 21:54

An idealized white body has a reflectivity $$r$$ of 1 and thus an emissivity $$\varepsilon$$ of 0 at all frequencies (the First Law, conservation of energy, states that reflection, transmission, and absorption must balance; the Second Law, entropy maximization or a prohibition from destroying entropy, states that a body at equilibrium in a thermal bath must absorb and emit equally, so absorptivity $$a$$ must equal emissivity $$\varepsilon$$).
So this white body (at temperature $$T$$) emits radiative flux $$\varepsilon\sigma T^4$$ (Stefan–Boltzmann constant $$\sigma$$), which is zero. In the absence of other heat transfer mechanisms (conduction, convection, latent heat, and so on), its temperature remains constant regardless of the conditions and surroundings, including impinging radiation. It shares this characteristic with the idealized transparent body.