Jed Rothwell wrote: > Robin van Spaandonk wrote: > >> . . . heat conducts very slowly compared to the timescale of a nuclear >> reaction. It conducts at the speed of sound. >> >> The speed of sound in metals is on the order of thousands of meters / >> second. If >> heat conducted at that speed you would burn your fingers the instant >> you put >> your teaspoon in your coffee. > > Huh. Good point. And yet I have often read that the heat conducts at the > speed of sound. Perhaps that means something like: the first temperature > rise (vibration) in a long copper bar reaches a sensor at the speed of > sound. Not that the entire thing comes up to the same temperature > instantaneously. Maybe it reaches the other end quickly but attenuates.
Any vibration -- including the vibration of atoms which is heat -- is presumably going to travel at mach 1. However, that's sort of like saying the EM wave when you hook up a battery goes through the wire at C (in the wire). It does, but that doesn't mean a capacitor hooked to the end of the wire is going to be fully charged Length/C seconds after you hook up the battery. The information that heat has started to flow travels that fast, but the actual heat flow rate (in joules/second/cm^2) is determined by other factors, and the rate at which the temperature rises depends on the heat flow rate and the thermal mass of the object being heated. Temperature goes up as the integral of the heat flow rate divided by the thermal capacity of whatever is being heated. Heat flow at each point on a bar will be proportional to the thermal gradient at that point, and in the example of the spoon, the gradient starts out at zero (when you first put the spoon in the coffee). As the temp rises along the bar the gradient increases and the flow rate increases; if the other end is held at a fixed temperature then it's a relaxation process and, in principle, it probably takes infinite time to actually finish "relaxing". (Not one of my more coherent responses, I'm afraid!) > > - Jed >
