Finally, suppose we have a material that violates Kirchhoff's law in detail, such that such that the total coefficient of absorption is not equal to the coefficient of emission at a certain T and at a certain frequency ν ν , then since it does not violate Kirchhoff's law when integrated, there must exist two frequencies ν ν 1 ≠ ≠ ν ν 2 , such that the material absorbs more than it emits at ν ν 1 , and conversely at ν ν 2 . Now, place this material in one Hohlraum. It would spontaneously create a shift in the spectrum, making it higher at ν ν 2 than at ν ν 1 . However, this then allows us to tap from one Hohlraum with a resonator tuned at ν ν 2 , then detach and attach to another Hohlraum at the same temperature, thus transporting energy from one to another, violating the second law.