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Author Topic: What is the speed of propagation of a thermal disturbance in a medium?  (Read 1613 times)

Peter Airey

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What is the speed of propagation of a thermal disturbance in a medium?
« on: 28/02/2011 19:30:04 »
Peter Airey  asked the Naked Scientists:

Dear Chris

Q. What is the speed of propagation of a thermal disturbance in a medium?

For example, if I take a copper rod one meter in length at room temperature, and I plunge one end in boiling oil, how long before the tiniest change in temperature can be detected at the other end?

Every day experience with objects heating and cooling might lead us to believe that the answer is of the order of a few millimeters or centimeters per second.

Consideration of some simplistic particle-motion models of heat conduction might  suggest a speed close to the speed of sound (particularly in the case of a gas).

A bit of googling turns up Fourier's equation for thermal conduction which, whilst apparently modeling reality fairly accurately, assumes a speed of propagation faster than the  speed of light (instantaneous propagation, in fact). Further googling reveals that the more recent hyperbolic forms of Fourier's equation allow for a finite speed of propagation, and here my google trail turns cold.

So, snail's pace or speed of light or what?...... can you give some typical values for this speed in different media and materials (assuming that it is a material property)? and more importantly, describe in plain English the physical conduction  mechanism(s) that justify the speed(s)?

Regards

Peter Airey

What do you think?
« Last Edit: 28/02/2011 19:30:04 by _system »

Soul Surfer

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• keep banging the rocks together
What is the speed of propagation of a thermal disturbance in a medium?
« Reply #1 on: 01/03/2011 22:28:57 »
The way you have stated this question makes it almost impossible to answer because in effect all three answers are correct.

You state "how long before the tiniest change in temperature"  this is not a precise measure and it depends on the sensitivity and response speed of your detector.  You also state "a medium"  quoting a copper rod (a solid electrically conducting medium) and you also include a gas.  (A fluid electrically insulating medium)

For transparent electrically insulating media like gases and glass rods radiation can be transferred through the medium when the heat is applied and so in theory the propagation of the smallest thermal signal will be at the velocity of light in the medium

For electrically conducting and opaque media the application of heat will cause a sonic thermal shock to be generated and so the smallest thermal signal will propagate at the velocity of sound in the medium.

Finally for a significant amount of heat to be transferred and a realistic temperature rise the standard Fourier diffusion equations will apply and the propagation velocity will be slow.

It is never a good idea to set extremal values for details like this because this takes things outside the limits of the standard approximations used to treat typical cases and causes all sorts of silly problems and arguments

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What is the speed of propagation of a thermal disturbance in a medium?
« Reply #1 on: 01/03/2011 22:28:57 »

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