Explanations of Prevost Theory of Heat Radiation

In 1792 Prevost applied the idea of dynamic equilibrium to radiation. He asserted that a body radiates heat at a rate which depends only on its surface and its temperature, and that it absorbs heat at a rate depending on its surface and the temperature of its surroundings. When the temperature of a body is constant, the body is losing heat by radiation, and gaining it by absorption, at equal rates.

It is easy to think of experiments which seem to support Prevost’s theory, and this can be well grasped if we imagine hot pies and cold ice-creams put into the same cupboard, which invariably means that the possibility of convection cannot be ruled out. For convenience, we shall take an old-fashioned, high vacuum, electric lamp, and put it in a can of water. We can find the temperature of the lamp’s filament by measuring its resistance. It would be discovered that, whatever the temperature of the water, the filament comes to that temperature, if it is left long enough. When the water is cooler than the filament, the filament cools down; when the water is hotter, the filament warms up.

In the abstract language of theoretical physics, Prevost’s theory is easy enough to discuss. If a hot body A is placed in an evacuated enclosure B, at a lower temperature than A, then A cools until it reaches the temperature of B. if a body C, cooler than B, is put in B, then C warms up to the temperature of B. we conclude that radiation from B falls on C, and therefore also on A, even though A is at a higher temperature. Thus A and C each come to equilibrium at the temperature of B when each is absorbing and emitting radiation at equal rates.

Now let us suppose that, after it has reached equilibrium with B, one of the bodies, say C, is transferred from B to a cooler evacuated enclosure D. it loses heat and cools to the temperature of D. therefore it is radiating heat. But if C is transferred from B to a warmer enclosure F, then C gains heat and warms up to the temperature of F. it may seem unreasonable to suppose that C stops radiating when it is transferred to F; it is more reasonable to suppose that it goes on radiating but, while it is cooler than F, it absorbs more than it radiates.

Prevost gave definitions to Absolute Equilibrium and Relative Equilibrium. Thus:

1.  Absolute equilibrium of free heat is the state of this fluid in a portion of space which receives as much of it as it lets escape to the surroundings.

2. Relative equilibrium of free heat is the state of this fluid in two portions of space which receive from each other equal quantities of heat, and which moreover are in absolute equilibrium, or experience precisely equal changes.

Note: What Prevost called free heat  is today known as electromagnetic radiation or photon gas which is a fluid, ray or free heat radiation.