As you can see from the voltmeter, I am getting 1.2 milliVolts. That's not much, but it is something. (The mass on the hot plate is just there to push the copper-steel junction down for good contact, if you were wondering.)
What you are seeing here is the Seebeck Effect (named after Thomas Seebeck). Two different metals together at two different temperatures can create an electric current. The effect is more pronounced with a larger temperature difference and some metal combinations work better than others—but there it is, your thermoelectric generator.
Actually, you can make a better generator by using a semiconductor instead of two different metals—but the two metal version is way easier to build. Here is a demo with a semiconductor. The device is sandwiched between two aluminum legs, with one leg in hot water and the other in cold water. The output from the device is going into a small electric motor on top.
So, how does this work? Why does a difference in temperature (for different metals) produce an electric current? I'm not going into the full story, since that would take way too long. But here is my super short answer: An electric conductor has free charges that can move about (somewhat). When you apply an electric field, these charges move and create an electric current. Normally, we think of these charges as electrons—but it could be something else. If you take a metal and make one end hot and the other end cold, the electrons on the hot side will have more energy and move about more. These hotter electrons spread out and on the cold end the electrons have less energy. The amount of charge separation depends on the particular metal.
Now take another metal with two ends at different temperatures. But since this metal is different than the first one, it will have a different charge separation on the hot and cold ends. When these different metals are put together, they will form a type of battery—not a very good battery, but still it's like a battery. And boom—there's your thermoelectric generator.
If you are thinking about building a thermoelectric generator to power your house, I have some bad news. These things are very inefficient. You need pretty big temperature differences to get something useful out of them. However, there is also some good news. These thermoelectric generators have no moving parts. No moving parts means they are small and quite reliable. And this is why they are used in some spacecraft (like Voyager, Cassini, and others). In order to make a temperature difference, the spacecraft will use a radioactive source that stays very hot—and really that's it. That's how your radioisotope thermoelectric generator (RTG) works. It's just like the paperclip and copper wire generator—except that it's way better.
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