A Good Absorber is a Good Emitter

where e is the emissivity of the object (e = 1 for ideal radiator). If the hot object is radiating energy to its cooler surroundings at temperature T_c, the net radiation loss rate takes the form

其中e是物体的发射率（e = 1 对理想辐射体）。如果热物体向其较冷的环境辐射能量，温度为Tc，则净辐射损失率可表示为

In this relationship the term with T_c represents the energy absorbed from the environment. This expression explicitly assumes that the same coefficient e applies to both the emission into the environment and the absorption from the environment. That is, a good emitter is a good absorber and vice versa; the same coefficient can be used to characterize both processes. Why is that true?

在这个关系中，T c 项代表从环境中吸收的能量。这个表达式明确假设相同的系数 e 同时适用于向环境发射和从环境吸收的过程。也就是说，好的发射体也是好的吸收体，反之亦然；同一个系数可以用来描述这两种过程。为什么这是正确的？

Perhaps the most fundamental conceptual way to approach this question is to observe that a hot object placed in a room must ultimately come to thermal equilibrium with the room. The hot object will initially emit more energy into the room than it absorbs from the room, but that will cause the temperature of the room to rise and the temperature of the object to drop. But when they reach the same temperature, we can conclude that the amount of energy absorbed on average is exactly the same as the energy emitted. That is, the expression above for net energy radiated to the environment must give us zero when T=T_c.

也许最根本的概念方法来处理这个问题是观察到，将一个热物体放在房间中，最终它必须与房间达到热平衡。热物体初始时会向房间辐射出比从房间吸收更多的能量，但这将导致房间温度上升，物体温度下降。但当它们达到相同温度时，我们可以得出结论，平均吸收的能量与辐射的能量完全相等。也就是说，上面关于净辐射到环境的能量的表达式，在T=Tc时必须给出零。

The above argument is based upon the Second Law of Thermodynamics in the form that states that heat will not spontaneously flow from a cold object to a hot object. If the absorption coefficient were higher than the emission coefficient for the object, then it could absorb net energy from the room even when its temperature were higher than the room.

上述论证是基于热力学第二定律的，该定律指出热量不会自发地从低温物体流向高温物体。如果物体的吸收系数高于其发射系数，那么即使其温度高于房间温度，它仍可能从房间吸收净能量。

But suppose you wanted to argue that a good absorber must be a good emitter based on the microscopic processes involving the atoms in the surface of an object. Then it becomes quantum question and involves the following ideas:

1. All electromagnetic radiation can be considered to be quantized, existing as photons with energy given by the Planck hypothesis, E=hf.

所有电磁辐射都可以视为量子化存在，其能量由普朗克假设给出，E=hf。

但假设你想从涉及物体表面原子的微观过程出发，论证一个好的吸收体必须是一个好的发射体。这便涉及量子问题，包含以下思想：

2. In order for a solid (or any matter, but I am assuming we are talking about solids) to absorb a photon of given energy hf , it must have a pair of energy levels separated by that amount of energy hf, so that the photon elevates the system from the lower member of the pair to the upper.

为了固体（或任何物质，但这里我假设我们讨论的是固体）能够吸收能量为hf的光子，它必须有一对能量差为hf的能量级，这样光子就能将系统从这对中的较低能级提升到较高的能级。

3. For visible light or near visible, then energy level pairs involved in most absorption are electron energy levels, so that when you absorb a green photon of photon energy 2.2 eV, you are causing an electron very near the surface of the solid to jump upward 2.2 eV. It can't do it unless there is a level at 2.2 eV up to receive it.

对于可见光或近可见光，参与大多数吸收的能级对涉及电子能级，因此当吸收一个能量为2.2 eV的绿色光子时，会使固体表面附近的一个电子跃升2.2 eV。除非存在一个2.2 eV的能级来接收它，否则无法实现这一过程。

4. If a surface is an ideal absorber in the visible, this implies that there is an abundance of available electron states so that a photon of any color in the visible spectrum can interact with electrons in the solid to elevate them to an available upper level. The implication is that any color in the visible spectrum can be readily absorbed, hence it is an ideal absorber, a perfectly black object.

4. 如果一个表面在可见光范围内是理想的吸收体，这意味着存在大量的可用电子态，使得可见光谱中任何颜色的光都能与固体中的电子相互作用，将它们提升到可用的较高电平。这表明可见光谱中的任何颜色都能被 readily 吸收，因此它是一个理想的吸收体，是一个完美的黑体。

5. The next step is not so obvious. If a pair of electron energy levels is available for absorption of a photon, it is also available for emission of a photon, i.e. , radiation. If it is available for an upward jump, it is available for a downward jump. One of Einstein's contributions was to show that for a given radiation, the probability for emission is the same as the probability of absorption. This fact is described in terms of the Einstein A and B coefficients and is very important in laser theory. The implication for the current question is that it constrains a good absorber to also be a good emitter. If the solid has lots of available electron levels for absorption, they will also be equally available for emission. To bring the discussion full circle, Einstein first derived his A and B coefficients from a thermodynamic argument like the argument above about thermal equilibrium before the actual development of the quantum mechanical ideas.

5. 下一步并不那么明显。如果一对电子能级可用于吸收光子，它也适用于光子的发射，即辐射。如果它可用于向上跃迁，它也适用于向下跃迁。爱因斯坦的一个贡献是证明对于给定的辐射，发射的概率与吸收的概率相同。这一事实用爱因斯坦A和B系数来描述，在激光理论中非常重要。对于当前问题的含义是，这会限制一个良好的吸收体也必须是一个良好的发射体。如果固体有大量可用于吸收的电子能级，它们也将同样适用于发射。为了将讨论闭环，爱因斯坦在热力学论证中首先推导出了他的A和B系数，这种论证类似于上述关于热平衡的论证，在量子力学概念实际发展之前。

The bottom line of this reasoning is that a good absorber of radiation will also be a good emitter. But the above is just the tip of the iceberg. For a black object, all visible colors are absorbed by electron jumps, but the elevated electrons usually follow a different path downward, cascading down in smaller jumps associated with perhaps infrared radiation. So we say that the light is absorbed and heats the object, associating heat with the infrared range of the electromagnetic spectrum. Nevertheless, it is a good emitter, just taking the light in as visible and reradiating it as infrared. For such a radiator at equilibrium, the fraction of light it emits in any wavelength range depends upon the temperature and for the ideal radiator is distributed in wavelength according to the blackbody relationship. The great complexity of dealing with all the quantum mechanisms and processes in a solid is the kind of thing that might have led Einstein to his purported preference for approaching problems from a thermodynamic perspective whenever possible.

这种推理的结论是，良好的辐射吸收体同时也是良好的辐射发射体。但上面的只是冰山一角。对于黑体来说，所有可见颜色的光都会通过电子跃迁被吸收，但升高的电子通常会沿着不同的路径向下跃迁，以较小的跃迁步骤释放，可能与红外辐射有关。因此，我们说光被吸收并加热物体，将热量与电磁波谱的红外部分联系起来。然而，它仍然是一个良好的发射体，只是将可见光吸收后重新辐射为红外线。对于这样的平衡辐射体，它在任何波长范围内的辐射份额取决于温度，并且对于理想辐射体，其波长分布遵循黑体关系。处理固体中所有量子机制和过程的复杂性，正是可能导致爱因斯坦倾向于尽可能从热力学角度来处理问题的原因。