Question

Suppose you have two black square plates, each at the same temperature, that are placed face to face with a small gap between them. They are both perfectly black, and one plate is emitting twice the radiation of the other. Explain why this would violate the second law of thermodynamics.

Answer 1

One black square plate emitting twice the radiation of a similar plate at the same temperature violates the second law of thermodynamics because they should be in thermal equilibrium, emitting and absorbing equal amounts of radiation.

Step-by-step explanation:

If two black square plates at the same temperature are placed facing each other, one plate emitting twice the radiation of the other would violate the second law of thermodynamics. This law states that heat transfer occurs from a hotter object to a cooler one, seeking thermal equilibrium. If both plates are at the same temperature, they must emit and absorb radiation equally, as described by Stefan's law which relates the power of emitted blackbody radiation to temperature with the formula P(T) = σ AT4. Essentially, one blackbody at equilibrium can't emit more radiation than another at the same temperature without external work being done, because this would suggest a spontaneous increase in energy without a corresponding temperature change, thus decreasing entropy which violates the second law.