Another argument that does not depend on the precise form of the entropy function, can be given as follows. Next, suppose we have a material that violates Kirchhoff's law when integrated, such that the total coefficient of absorption is not equal to the coefficient of emission at a certain T , then if the material at temperature T is placed into a Hohlraum at temperature T , it would spontaneously emit more than it absorbs, or conversely, thus spontaneously creating a temperature difference, violating the second law.