Perfect Blackbody

Definition

A body which absorbs the entire radiant energy incident on it is called an ideal or perfect blackbody. For a perfect blackbody the coefficient of absorption $a = 1$, and therefore $r = 0$ and $t_{r} = 0$.

Any surface that absorbs all the energy incident on it, and reflects none, therefore appears black — unless its temperature is so high that it is self-luminous. Lamp black and platinum black absorb nearly 97% of the incident radiant heat and so closely resemble a perfect blackbody. No real surface is a perfect blackbody, so for study of radiation an arrangement is used which behaves as one.

Ferry's blackbody

Diagram in words: a double-walled hollow sphere shown in section. The space between the two walls is evacuated and the outer surface is silvered; the inner surface of the sphere is coated with lamp black. A tiny hole (aperture) is made in the wall, and directly opposite the aperture, on the inner surface, there is a small conical projection pointing inwards. An incoming ray is drawn entering through the aperture, striking the conical projection obliquely, and then undergoing several successive reflections inside the sphere before being completely absorbed. Labels: aperture, conical projection, lamp black coating, evacuated space, silvered outer surface.

Construction and working:

i. Ferry's perfect blackbody consists of a double-walled hollow sphere having a tiny hole or aperture, through which radiant heat can enter.

ii. The space between the walls is evacuated and the outer surface of the sphere is silvered. This prevents loss of heat from the sphere by conduction, convection and radiation, so its temperature stays uniform.

iii. The inner surface of the sphere is coated with lamp black, which is itself a very good absorber.

iv. There is a conical projection on the inner surface of the sphere opposite the aperture. The projection ensures that a ray travelling along the axis of the aperture is not incident normally on the surface and is therefore not reflected back along the same path.

v. A heat ray entering the sphere through the aperture suffers multiple reflections at the lamp-black surface and is almost completely absorbed inside. Radiation entering through the small hole has a negligible chance of escaping back through it.

vi. Thus the aperture, and not the sphere itself, behaves like a perfect blackbody.

vii. The effective area of the perfect blackbody is equal to the area of the aperture.

In a similar construction Wien used a cylindrical body with a vertical slit as the aperture, which gives a greater effective area as a perfect blackbody.

Cavity radiator

A similar action is obtained from a cavity radiator, which consists of a block of material with an internal cavity, the inner and outer surfaces being connected by a small hole. Radiation falling on the block that enters through the hole cannot escape back from it, so the cavity acts as a blackbody. When the block is heated to a high temperature, thermal radiation is emitted; this is called cavity radiation and resembles the radiation emitted by a blackbody. Its nature depends only on the temperature of the cavity walls and not on the shape or size of the cavity or on the material of its walls.

Good absorbers are good emitters

Consider two objects, opaque to thermal radiation, at the same temperature and with the same surface area, one well-polished and the other painted black. The well-polished object reflects most of the energy falling on it and absorbs little; the black painted object absorbs most of the radiation and reflects little. For the temperature of each to be maintained, the rate of emission must equal the rate of absorption. The black painted object absorbs more, hence it must also radiate more. Therefore good absorbers are always good emitters and poor absorbers are poor emitters. Further, since each object must either absorb or reflect the radiation incident on it, a poor absorber is a good reflector and vice versa; hence a good reflector is also a poor emitter. This is the reason for silvering the walls of vacuum bottles and thermos flasks, and for blackening the bottom of a cooking utensil while polishing its top.

Standard results

• Perfect blackbody: absorbs the entire radiant energy incident on it; $a = 1$, $r = 0$, $t_{r} = 0$.

• Realised in practice by Ferry's blackbody or a cavity radiator; the aperture behaves as the blackbody and its area is the effective area.

• At a given temperature a perfect blackbody has the maximum emissive power of any body.

• Good absorber $\Rightarrow$ good emitter; good reflector $\Rightarrow$ poor emitter.