What is the speed of heat?

[Bella]

I purchased this cold heat soldering iron today and basically it heats up really fast. Now my friend asked me "whats the max speed for something to heat up?" I told him it was the speed of light or probably very close under it.

Is the speed of heat related to the speed of light?

[Vagelford]

No. It isn't the speed of light that is related with thermal phenomena.
The speed of heat is related with the maximum speed that you can carry energy from one part of the medium to the other, and that is the speed of sound in the medium. Energy is carried with phonons, which are the energy quanta. But in solids things are generally a little complicated. It depends on if the solid is a conductor or an isolator. In conductors the free electrons play an important part in the thermal conductivity.
But in general the key speed is the speed of sound.

[_mark_]

I thought about something like this a while back but didn't go all the way with it, was going to post it, will do now :)

Rewriting the ideal gas equation as P/rho = T and affecting a small change in all variables you get
delta T = deltaP / delta rho
So the change in temperature is proportional to the square of the speed of sound in the gas, the rate of change of temperature should be proportional to the twice the velocity times the 'acceleration' in the gas??

I didn't know if you could just say that sort of thing, here with conductors and things the equation of state would be more complicated than PV=RT though the drude model was similar

Its not too off topic so an answer to whether the above is right would be nice

[Vagelford]

Actually a variation of P/rho = T would give

dP/rho - P*drho/rho^2 = dT

so if you wrote something about the speed of sound it would be

dP/drho = (u_s)^2 = P/rho + rho*dT/drho

[_mark_]

Gotcha, yeah mathematical variation <> small changes, dbar and all that. Thanks

[Bella]

Speed of sound.... gotcha thanks! The rest of that stuff... I have no idea what it means.