# Reversed First Joule's Law : heating a resistor produce voltage?

I was discussing about the theory that claims that "every emitter also behaves like a receptor": Are emitters always receptors? I was brilliantly told that this theory would be false for fluorescent lights and also for resistors, because of entropy messing with time-reversed operations (condensed version!).

However, as I'm curious by nature, I made this little experiment: heating a 330 Ohm resistor with a flame and measure its voltage with a cheap multimeter. What a surprise to discover that some current flowed from this hot resistor!
At 20°C, I measured 0.0mV, after ±3 seconds of heating it was 0.6 mV (current around 1μA).

Have I just discovered some kind of "reversed" first Joule's law? :)
Or did I made some logical, methodological or experimental mistakes?

• I always love the handful of questions we get in the form "I did an experiment because I was curious, and the results were surprising. Help me understand!" They don't happen often enough. – Cort Ammon Sep 8 '17 at 23:44
• Perhaps you made a thermocouple accidentally? – immibis Sep 11 '17 at 0:54

Nice experiment!

But think: why would a current flow in a particular direction and not the other? Is the system somehow asymmetric? As the other answers have suggested, this is probably a thermo-electric current due to the Seebeck effect (a complication I didn't want to get into for your other question).

But now that we're there, here's another thing to try: can you change which direction the current flows by how you are heating the resistor? Does the magnitude or direction of current change when you heat one wire of the resistor versus the other? The Seebeck effect comes into play at electrical interfaces, where there's asymmetry, so the direction of the interface would determine the direction of the current!

The asymmetry issue is another way how you can see that you can't reverse the standard Joule heating: You will get the same heating for a current running either direction through the resistor. But if you cool the resistor to try to undo it, which way would the resulting current flow?

I believe it may have been a manifestation of the Seebeck effect.

As some dissimilar metal to metal junction was heated in your setup, it started to generate a small voltage difference somewhat proportional to the temperature difference. Essentially it was probably a really poor and non-linear thermocouple.

Not really the reverse of the Joule Heating though.

A lot of the other answers are describing what you saw. I will describe what you were looking for. You noticed that in joule heating, the energy from moving charges gets converted to thermal energy. You can ask if the thermal motion of atoms in the resistor can create a voltage. The answer as you guessed is yes. However, since the thermal motion of the atoms is disorganized, you will not get a steady voltage pointing in one direction along the resistor. Instead, you will get a small fluctuating voltage across the ends of the resistor. The variance of the distribution of voltages you will get is proportional to the temperature, so heating the resistor up will indeed increase the RMS voltage you observe. This effect is called Johnson noise.

Since this noise is weak, you will need an amplifier to measure it. Here is a lab manual for a Johnson noise experiment from MIT I found online if you want to try to do it yourself or see how it would be done.

• I think the Seebeck effect is a more likely explanation for the current the OP measured – a cheap multimeter meant to measure DC would likely not have enough bandwidth to gather significant Johnson noise. But this is still the best answer to the theoretical idea behind this question IMO. – leftaroundabout Sep 9 '17 at 21:12

If a resistor has a temperature gradient, then the thermal velocity of the electrons in the hot part is larger than the thermal velocity of the electrons in the cool part. This causes a density imbalance, which in turn creates a small electric field, and in turn, a current.

I don't know if that's what's happening in your case, but it would be interesting to see if you could try to heat one end of the resistor more than the other and observe whether the measured voltage switches sign.

To clarify, though, this is not some kind of reversed Joule's law, which is another example of your aforementioned time-irreversable phenomena.

In usual ohmic conductors, subject to relative small potential differences and in room temperatures, there are two different motions performed by the free electrons: the thermal motion of the electrons (disoriented motion with typical values of speed at the order of $\cong 10^6 m/s$) and the drift motion of the free electrons (oriented motion with typical values of the magnitude of the drift velocity at the order of $\cong 10^{-3} m/s$).

The joule effect "absorbs" kinetic energy -from the whole of the conductor's mass- from the drift velocity (through collisions of the free electrons with the ion-grid) and "turns" it into heat. While the thermoelectric effect is actually the creation of voltage out of the temperature difference (and not the temperature itself) between two - spatially discrete- parts of the conductor. These two phenomena are not inverse to each other. Quoting from Wikipedia:

The Peltier–Seebeck and Thomson effects are thermodynamically reversible, whereas Joule heating is not.

## protected by Qmechanic♦Sep 9 '17 at 10:24

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