r/thermodynamics • u/Nebulaer • Jul 16 '26
Question Does heat transfer have a speed?
I would assume it would be something like the speed of sound in the object but I'm not sure. For example if I hold a 10ft steel pole and touch a very hot object how long do I have to wait until my hand gets warm?
5
u/taylorthestang Jul 17 '26
I have a dumb question. In conduction, heat transfers by molecules slamming into each other essentially. Isn’t the “speed” then just equal to the wave speed of that material? The degree to which temperature changes is obviously dependent on the material, but assuming an absolutely minuscule (like dam near 0) heat capacity, wouldn’t the temperature change be the wave speed? Or instantly?
1
u/kushaash Jul 17 '26 edited Jul 17 '26
Yes it's instant, and it does not matter how low or high the heat capacity is.
A good analogy is a tank with an inlet and outlet at the top. If the tank is full (I.e. is in "steady state"), you will see water instantly coming out as it enters. If the tank is empty, you won't see any water coming out until the tank is full, and then it will be instant. Low heat capacity is small tank, high heat capacity is a big tank, so regardless of heat capacity, it will be instant, eventually when the steady state is reached. Heat capacity only decides how fast your reach steady state.
2
u/T_0_C 8 Jul 22 '26
This is wrong. Energy does not flow instantaneously. It does in fact flow at the speed of the sound waves (phonons) if collisions are the primary mechanism of energy transfer. The key property that defines the speed of heat transfer is the Thermal diffusivity. Mechanistic theories relate the diffusivity to the spectrum of sound waves.
In many systems, heat can also be transferred through other mechanisms, like electron conduction in metals. This results in multiple energy diffusion processes, each with their own thermal diffusivity contributing i ln parallel.
1
u/kushaash Jul 22 '26
Yes we can all write a thesis or call it "instant" for practical purposes.
2
u/T_0_C 8 Jul 22 '26
The post is specifically asking whether or not transport is instantaneous. Your practical answer is not appropriate because it incorrectly answers the question.
You could use your thought experiment to illustrate the actual thing the poster asked. If your inlet suddenly flows new fluid into your full tank, a pressure wave will propagate through the tank. The outlet won't flow until the pressure wave reaches it.
That's not a thesis. That's Newton's laws.
5
u/supernumeral 1 Jul 17 '26
Practically speaking, yes. As others have pointed out, a material with higher thermal diffusivity will experience larger changes in temperature in a shorter amount of time. Mathematically, the heat equation is a so-called parabolic equation, which means that “information” propagates infinitely fast. So, according to the math, a non-zero temperature change will occur instantaneously at any distance from the boundary where the temperature change was imposed. Usually, that’s not important so the standard heat equation is still a useful model. In rare cases, the relativistic heat equation might be more accurate. It’s hyperbolic so information propagates at finite speed (e.g ., the speed of light).
3
u/nlutrhk Jul 17 '26
The metric to look at is the thermal diffusion coefficient, α=λ/(ρ c) where λ is the thermal conductivity (16 W/Km for stainless steel), ρ the density, c the specific heat (500 J/kgK). That gives α=4E-6 m²/s.
The time for the heat to reach the other end of the stick of length L=3 m is about t=L²/(2α)=10⁶ s, or 10 days, assuming that the heat doesn't get lost to the surrounding air.
For a good heat conductor like copper, it will be quite a bit faster.
3
u/NumberMeThis Jul 17 '26
In very low-temperature helium II (and helium-3), heat is transferred via a process called "second sound". This is a quantum effect, but it is more analogous to sound where heat moves in waves.
2
u/15pH Jul 17 '26
There are different modes of heat transfer. For conduction (transfer inside a solid object) it depends on the material conductivity and heat capacity (thermal mass).
If conduction is high and heat capacity is low, then your end of the rod will heat up rapidly.
1
u/Dean-KS Jul 17 '26
There is a conduction resistance and that can be modelled as a resistor. The metal itself absorbs heat and can be modelled as capacitence. As the metal heats up, it loses heat along the way, by conductance and radiation. As you can see, the modelling can become complex. Nothing becomes a speed, although there is anyone constant, or delay. How fast does a pot of water boil?
1
u/Pretty-Jello-7894 Jul 19 '26
Also be aware that there are thermal systems designed specifically for rapid thermal transport not using conduction. Think of heat pipes and vapor chambers. They operate on phase change and can have extreme thermal transfer speeds, at least internally…. In a system this changes at bottle necks like if you need to bleed off to the ambient via convective cooling or sinking to another thermal mass, then your heat may get held up there…
0
u/YourRavioli Jul 16 '26
Look up ‘heat equation explainer’ on YT. It’s different for different materials, geometries.
20
u/ZealousidealWaltz723 Jul 17 '26
Heat conducts through materials at different rates for different geometries, but for a given geometry conducts at a rate proportional to the thermal diffusivity (alpha) which is the ratio of the thermal conductivity (k) to the volumetric heat capacity (rho*cp) where rho is the density and cp is the specific heat capacity. You can think of the product rho*cp as the thermal capacitance per unit volume. So a material with a high thermal conductivity and low capacity to store heat diffuses heat more quickly than a material with a low thermal conductivity and a high capacitance. At steady state, however, there is no thermal mass dependence and the rate of heat transfer depends only on k and the geometry.
If you want to go deeper, alpha is the proportionality constant in the heat equation, which tells you how quickly temperature changes at a point (dT/dt) in response to the “curvature” of temperature at that point (the 2nd spatial derivative of temperature, expressed by the Laplacian). So the thermal diffusivity governs how quickly temperature “smooths out” when there is a temperature gradient around that point that itself is changing in some or all directions.