everything you know is wrong - part 49

answers to those doggone thermal design questions by tony kordyban, author of
hot air rises and heat sinks: everything you know about cooling electronics is wrong and more hot air

index to previous columns.

dear conundrum-buster,

i have been thinking a lot about thermocouples. it seems from your articles that they could be used to create energy out of nothing. yeah, i know about conservation of energy (“it’s not just a good idea, it’s the law.”) that’s what’s bothering me. if thermocouples work the way that you say, then i think i’ve found a way that they can violate conservation of energy.

that puts me in a quandary, because i wouldn’t know who to trust – you or the laws of physics. anyway, here’s my idea for free energy: start with a thermocouple in a well insulated container of molten lead and another identical container with lead at the same temperature but with a heating element. connect the thermocouple and heater in a complete circuit. intuitively it seems that the thermocouple would generate a current which would be dissipated in the heater. the container with the heating element would get hotter and hotter, increasing the temperature difference between the two containers, making the current in the thermocouple bigger and bigger. that would make more heat in the heating element, driving the temperature higher, with no limit in sight. the temperature difference between the two containers could then be used to drive some kind of heat engine. so i’ve created useful energy from nothing, just using a thermocouple and a heater.

somebody will probably say this doesn’t work because of entropy, or some other concept nobody can understand intuitively. can you show me in layman’s terms where is the flaw in my idea?

perpetually intrigued by perpetual motion

dear perp,

there is a very simple hole in your argument. you start out with two containers of molten lead at exactly the same temperature. i’m not sure why molten lead. i prefer melted velveeta cheese, but that is not the point. for some reason you start with the two containers at the same temperature.

if you dunk the one end of your thermocouple in each of the containers of molten lead, then the thermocouple junctions will be at the same temperature. without a temperature difference, the thermocouple does not generate any voltage. zip, nada, goose egg, zero, zilch. no voltage, no heat produced by the heater element. nothing happens. the containers start at the same temperature, and stay that way. the law of conservation of energy is not even having a nose thumbed at it.

defender of the law,

ok, you got me on that one. i forgot about needing a temperature difference to get the circuit going. i was all hung up on showing how a thermocouple and a heater element could create a temperature difference out of nothing, violating the laws of thermodynamics.

but you didn’t really get to the meat of my question. let me start over. let’s say that we have two containers of molten lead (or velveeta) in perfectly insulated surroundings. one container is at 500°c, and the other is at 510°c to start. i dunk in my thermocouple, and put the heater element into the 510°c container. now there is a 10°c difference between the two junctions, which make a voltage, which creates a current in the circuit. the current in the heater element makes heat, which goes into the molten lead, increasing its temperature. that makes the temperature difference between the two containers go up, which increases the voltage, increasing the current, increasing the heat generated by the heater element. theoretically, the temperature of the hot container will increase more and more until something burns up. or i could use the temperature difference between the two containers to drive a steam engine to generate electricity. that would be an endless supply of electricity created by a passive pair of wires.

obviously this shouldn’t work. but why?

perpetually perplexed

dear perp,

i was hoping you wouldn’t notice that i slipped out of your thermodynamic trap a little too easily. this column is supposed to be about cooling electronics, not thought experiments in physics. but since thermocouples and thermoelectric coolers are common tools of the trade, and there is a lot of magical thinking about how they work, i’ll tackle your question.

i had considered referring you to thermocouples for dummies, but after i tried to read it myself, i decided that it had not been dumbed down enough. i would have to write my own even dumber version called “thermocouples for engineers.”

thermocouples for engineers

have you ever noticed that the really good conductors of heat, like copper and aluminum, are also pretty good conductors of electricity? that is not a coincidence. electrons carry most of the heat that conducts through a piece of metal, the very same electrons that participate in electric current when a voltage difference is imposed on the piece of metal. think of the “free electrons” in metal as being loosely bound to the metal atoms in the crystal structure. they are kind of like frosting on a cake – stuck in place, but fairly easy to push around. it takes only a small voltage to get the electrons to flow in a copper wire. much smaller than the voltage it takes to budge electrons in a piece of vinyl.

so if heat flows by moving electrons around in metal, and voltage moves electrons around in metal, then there is bound to be some kind of interaction between heat flow and electricity in metal.

this happens even when there is only one kind of metal. there is nothing magical about having two different metals in a thermocouple. when a temperature difference is imposed on a hunk of metal, a voltage difference forms. let’s “impose” such a temperature difference on the bar of iron in figure 1, say, by sticking one end in a fire and dunking the other end in a bucket of ice water. heat will conduct through the iron bar from the fire to the ice water. most of the heat is conducted by the free electrons in the layer of “frosting”. this heat flow makes the electrons tend to bunch up at the cold end of the iron bar, giving the cold end a small negative electric charge, and the hot end a small positive charge.

figure 1. when heat flows through a metal bar, the heat is carried by the free electrons from the hot to the cold end. that builds up a voltage difference between the two ends.

you might be wondering how the heat keeps flowing once the electrons are all stuck at one end of the bar. it’s not like the electrons flow down the rod like water through a pipe, carrying the heat with them. after all, the end of the pipe is a dead end, and there is no place for the electrons to flow to, so the flow would have to stop once they all get to the cold end. heat conduction works more like the balls in the executive desk toy in figure 2.

figure 2. a model of heat conduction by free electrons in a metal bar.

the electrons at the hot end get bumped by the highly energetic gas molecules from the fire, and they in turn smack into their neighboring electrons a little further down the rod, transferring their energy to the next one and the next one and so on down the bar. the last electron swings out and smacks a molecule of water in the ice bucket, giving up its energy and swinging back into the iron rod. there is a net displacement of the electrons toward the cold end, because that end electron, after giving up its energy, doesn’t come colliding back with the same energy it had when it swung out. think of it like the whole assembly of pendulums is leaning toward the cold end. that’s what makes the cold end negative and the hot end positive.

just how many volts per degree c do we get from our bar of iron? not much, on the order of a handful of microvolts per degree. the exact number depends on the material the bar is made from, and its absolute temperature. that material property, the number of volts per degree of temperature difference, is called the seebeck coefficient. it differs quite a bit from material to material, and is not linear with temperature. but i am getting ahead of myself here.

ok, we have an iron bar with fire and ice imposed on it, and there is a tiny but measurable voltage difference between the two ends. why don’t we just complete the circuit and let current flow?

here is the trick: what are we going to use to complete the circuit between the hot and cold ends of the iron bar? a metal conductor, of course. suppose we take another iron bar, and weld the ends of it to the ends of our first iron bar, to form the circuit shown in figure 3.

figure 3. making a thermocouple circuit out of two identical materials, like iron and iron, doesn’t get you very far in getting current to flow.

the second iron bar also runs from the fire into the ice, so its electrons all scrunch over to the cold end. since the material is exactly the same as the first bar, the voltage between the two ends is the same as the first bar, and in the same direction. no current will flow. it is like hooking up two 1.5v batteries like in figure 4.

figure 4. what happens if you hook up two batteries of the same voltage like this? the voltage of one opposes the voltage of the other, and there is no current flow. this is what happens when you make a thermocouple out of two wires of the same material.

but current doesn’t flow in the battery circuit of figure 4 only because the voltages cancel out. what if you hook up two batteries of different voltage values? like in figure 5?

 figure 5. in this circuit there is a net voltage of 4.5v, so current will flow. i don’t recommend breadboarding this circuit.

where can we get the equivalent of our 6v battery to go with our iron bar? that is where the “dissimilar metals” of the thermocouple recipe comes in. pick any other metal besides iron – even a different alloy of iron. as long as it has a different seebeck coefficient, it will produce a different voltage than the iron bar. the voltage will still be in the same direction as the iron bar. but as long as the magnitude of the voltage is different, there will be net voltage difference in the circuit, and current will flow.

 figure 6. doesn’t this picture remind you of the picture of the 6v and 1.5v batteries? make the return conductor from another metal, such as copper, and now you get a voltage difference that makes current flow. in this rather vaguely specified example, there is a net voltage across the iron bar of 0.000045v, driving current to flow in the circuit.

now you know everything about thermocouples. let’s have a quick review of my theory of thermoelectricity before we go on to something a little fancier (peltier coolers.)

• heat is conducted through metal by the movement of free (cake frosting-like) electrons
• a temperature difference across a piece of metal makes the metal act like a battery.
• the volts per degree (the seebeck coefficient) is unique to each type of metal.
• pair up a couple of these batteries of different metals, and there is a net voltage proportional to the temperature difference.
• if the circuit between these two dissimilar batteries is closed, a (small) current will flow.

that’s a lot to learn from the ball bearing pendulum executive toy. but i still haven’t come close to answering your question about the conservation of energy. there is one more piece of the puzzle yet to explain.

the peltier effect

it is now second nature for us that a temperature difference will cause electrons to move in a metal wire. does the same thing work in reverse? you bet. impose a voltage on a metal wire, and the electrons moving through the wire carry heat energy around as they go.

perhaps you never noticed that happening when you hooked up a battery to a light bulb. if the whole circuit is made out of a single kind of metal, such as the copper you normally find on the shelf, then there isn’t anything to notice. the electrons flow around the circuit, carrying the same amount of heat around and around like carousel horses carrying the same kids around and around in a circle.

to see anything “cool” happening, you need to make the circuit out of two dissimilar metals. why?

first let’s ask another question: how much heat energy does an electron carry when it is flowing through a metal wire?

an amount so tiny that it makes you last pay raise seem gigantic next to it. it is tiny, but a definite amount. and the amount of heat a moving electron carries depends on the metal that it is flowing through. remember the seebeck coefficient from the iron bar? it was a material property of the iron that was a measure of the voltage produced by the temperature difference.

there is another material property, related to the seebeck coefficient (s), that tells us effectively how much heat is carried by each electron. it is the peltier coefficient (p), defined as:

p = thermal current density / electric current density = t x s

where t is the absolute temperature of the metal in kelvins.

the amount of heat carried by each electron is proportional to the seebeck coefficient of each metal. since the seebeck coefficient is different for each metal, that means the amount of heat per electron is unique to each kind of metal, too.

that doesn’t seem to be very intuitive to me. i thought an electron was an electron, whether it’s in copper or platinum. apparently, the amount of heat carried by the electric current depends on how the electrons form their cake frosting on top of the atomic crystal structure. let’s not worry about that (since i have no simple explanation for it).

in any case, why do we care how much heat each electron carries? because it is the difference between this value from metal to metal that makes the peltier effect work.

in my iron/copper thermocouple circuit in figure 6, i made up some voltage numbers as an illustration. i said that for a given temperature difference between fire and ice, the copper bar had a voltage difference of 0.00006v, and the iron bar had a voltage difference of 0.000015v. (these numbers are totally made up! remember, i haven’t even told you the value of the temperature difference.) the seebeck coefficient (let’s call it s for short) for copper is about 4 times larger than iron. by my argument above, that means each electron in the copper bar carries about 4 times the heat energy as each electron in iron.

assuming these values are correct (and i have not even checked), then let’s make a circuit out of iron and copper wire, like the one shown in figure 7. notice the white background of the picture. the fire and ice have been tossed out, and the whole circuit starts out at the same temperature – room temperature, if you like. we impose a fixed dc voltage on the circuit with a battery, and current begins to flow, limited by the resistance of the wires themselves.

if you are keeping a close watch on things with your infrared vision, you will begin to notice something weird happen. one of the junctions (the joint between the iron and copper wires) begins to cool down below room temperature, and the other junction begins to heat up above room temperature. the current flowing in the circuit is creating a temperature difference between the two ends. the thermocouple is working in reverse.

figure 7. electrons flow from minus to plus, remember? here is the beginning of a simple solid-state refrigerator, believe it or not. if the battery were reversed, the cold and hot junctions would switch around, too.

where does the temperature difference come from? you definitely don’t see this happening in a circuit made out of copper wire alone.

the explanation is simple, if you can imagine yourself driving a van the size of an electron. you are driving along the copper wire after leaving the negative side of the battery, carrying your full capacity of heat passengers, which we will represent as four hefty young soccer players. each player represents some heat energy, say 1 femto-foot-pound, if you need a concrete number to think about.

everything is fine until you get to the end of the copper wire, and you want to transfer over to the iron wire to continue your journey. except that in the iron wire, you are limited by local regulations (the peltier coefficient of iron) to carrying only one soccer player. three of your heat passengers have to get out and walk at the intersection between the iron and copper highways. you drop off the three extra passengers.

your electron/van has to dump heat to flow from the copper to the iron. you, and every electron in line behind you, have to dump some heat at the copper/iron junction. that extra heat raises the temperature of the junction.

now you drive along the iron wire with one soccer player, perfectly happy until you get to the next junction with the copper wire. but before you can continue into the copper wire, you have to comply with the local car-pooling regulation that requires you to have four passengers. (remember, each electron in copper carries four times the heat that it does in iron, at least in this example.) you need to pick up three more soccer players before you can continue. since on every trip from that junction, you remove heat, you are cooling the junction, reducing its temperature. every electron drives up empty, and leaves full.

one junction cools down and the other heats up. that heating is different from the joule heating you are familiar with. current through a resistance produces heating. joule heating is also happening due to the resistance of the wires, but that heating is distributed through the whole length of both wires. the peltier heating happens only at the junction between the two metals.

the puzzle solved, at last

now we have enough pieces of the thermocouple puzzle to explain your molten lead (or, as i prefer, melted cheese) puzzle of ever-increasing temperature.

let’s show your infinitely increasing temperature difference machine in figure 8. there is a fondue pot of melted cheese at 120°c (the cold one) and a second one that starts out at 130°c, a little bit hotter. we make an iron/copper thermocouple circuit, with one extra feature: it has a resistive heater element in the circuit, and it is located in the hot fondue pot.

figure 8. the infinitely increasing temperature difference machine.

the 10° temperature difference across the thermocouple creates a voltage, and the voltage produces a current. the current passing through the heater element releases heat energy to the hot cheese pot, making it even hotter. this will theoretically keep increasing the hot cheese temperature, increasing the voltage, increasing the current, increasing the heater element heat, and so on, until something burns up.

this won’t happen. the electric current in the thermocouple is actually cooling the hot cheese at the same time that it is heating it up! the circuit in figure 8 is the same as the circuit in figure 7, except that the battery has been replaced by the voltage of the thermocouple itself. the electric current still removes heat from the junction on the right, and releases heat at the junction on the left. the peltier cooling effect (electrons arriving empty and leaving full) happens whenever there is electric current in the circuit, even if there is no external power source to drive it.

the peltier cooling effect is the feedback mechanism that keeps the thermocouple from turning a tiny temperature difference into a big one. what will really happen if you build such a circuit between two pots of cheese is that heat will conduct through the thermocouple wires from the hot cheese to the cold cheese, until the two pots are at the same temperature.

free energy is a difficult dream to let go of. just ask those cold fusion guys, of which one of them is still trying to make the thing go. maybe you think if you just pick the right combination of metals, or try semiconductors which use positive charge carriers for electric current, maybe you could still come up with a way for the thermcouple to create energy from nothing. don't waste your brain power on it. i used copper and iron as examples here. but the point is that the mechanism that creates the voltage in the thermocouple is the same mechanism that drives the peltier cooling. they are both dependent on the relative seebeck coefficients of the two conductors. whatever combination of metals you put together, the heat generated by the thermocouple current will be cancelled out by the peltier cooling.

if that is too disappointing or boring, you can always use the melted cheese to make nachos (don’t eat cheese that has been in direct contact with copper. copper is toxic. at least more toxic than american cheese.)

once again, the universe is saved, thanks to that ball bearing pendulum executive desk toy thing.

the straight dope on tony kordyban

in those twenty-odd years tony has come to the conclusion that a lot of the common practices of electronics cooling are full of baloney. he has run into so much nonsense in the field that he has found it easier to just assume "everything you know is wrong" (from the comedy album by firesign theatre), and to question everything against the basic principles of heat transfer theory.

tony has been collecting case studies of the wrong way to cool electronics, using them to educate the cooling masses, applying humor as the sugar to help the medicine go down. these have been published recently by the asme press in a book called, "hot air rises and heat sinks: everything you know about cooling electronics is wrong." it is available direct from asme press at 1-800-843-2763 or at their web site at http://www.asme.org/pubs/asmepress order number 800741.

this has been followed by his best-selling sequel, aptly titled "more hot air," from asme press. (it is the best-selling sequel he has ever written.)

this advice column is an extension of that educational effort. if you have a doggone thermal design question that you'd like tony to answer in this column, please post it to the tony kordyban discussion group here on coolingzone, or email me direct at [email protected]. unlike dear abby, though, he won't necessarily limit himself to questions from actual people, but might resort to making some up to teach a lesson once in a while. engineers are sometimes too shy to share their embarrassing dumb questions in public.

copyright by tony kordyban 2005 electronic publishing by coolingzone.com with permission of author. all other rights reserved by tony kordyban.