system
Given the following post, respond as if you're commenting on Reddit:
human
Planck's quantum hypothesis proves that a body can't emit radiation beyond a certain frequency, but this still means that it will emit waves in ALL THE POSSIBLE FREQUENCIES below this limit. So wouldn't the body still be losing energy at an infinite rate?

Or am I misunderstanding something?
gpt
Your first sentence is simply not true. A blackbody emits at all frequencies. Where did you get that there is an upper limit?

As per your last question, just because it emits at all frequencies it doesn't mean the energy is infinite. The total intensity is the integral of the spectral insensity per unit wavelength. In symbols:

I = integral of dλ B(λ) from 0 to infinity

Where B (λ) = dI/dλ and dI is the intensity emitted between wavelength λ and λ+dλ.

Planck's hypothesis allows you to calculate a form for B(λ) (the blackbody spectrum) which is such that the above integral is finite, even though you integrate over an infinite domain. Instead, the older Rayleigh-Jeans law provides a B(λ) whose integral diverges when integrated down to λ-> 0 (ν -> infinity), which is the ultraviolet catastrophe. That's why under Planck black bodies actually *stop* emitting the infinite energy they should have in the classical theory.