I've been reading through the Feynman lectures (almost done with Volume 1), and I have been trying to prove everything to myself. I have a bit of a problem now though, in Chapter 41 on Brownian motion, Feynman shows what the voltage in an LRC circuit is due to thermal noise, and then says that the power distribution (with respect to angular velocity) is the following: P(w)dw=(2/pi)ktdw Now I have two problems. First, I do not understand where this comes from. At that point he says merely that it will be proven later, and the later proof is unhelpful and vague. The second problem is that the above formula does not check out with dimensional analysis. Power is in terms of J/s, kt is in terms of J, dw is /s, and cancels on both sides. Leaving J/s=J Is it wrong or am I missing something? The later explanation that is given is that the noise generator in a circuit with resonance (adjustable) can be described as the signal received from an antenna due to thermal radiation emitted from the surrounding environment. This he shows (and I follow the explanation for this part) to be proportional to I(w)=w^2*(kt)/(pi^2c^2), and the correction for high temperature or low frequency is also shown, where I is the intensity of the radiation. It seems to me that Power=Area*Intensity, and so it would depend on the size of the antenna. Can anyone explain this?