How do the heating elements work? It's through a process called joule heating. A joule is a derived unit of energy named after the physicist James Prescott Joule. A joule is equal to the work required to move an electric charge of 1 coulomb through an electric potential difference of 1 volt. It's also the amount of energy expended to produce 1 watt of power for 1 second.
Joule heating relates to another aspect of electricity -- electrical current resistance. We call material that allows electricity to flow through it a conductor. But most conductors aren't perfect -- they have what we call resistance to electricity flow. This resistance results in electrical power loss. But the laws of thermodynamics state that you can't destroy energy, so where does the power go? It converts into heat.
The amount of heat a conductor generates through resistance depends upon several factors. Different materials have different levels of resistance. The gauge -- or thickness -- of the conductor also affects its resistance. Thicker conductors have less electrical resistance than thinner wires. The length of the conductor also impacts its electrical resistance. The further electricity has to flow through a conductor, the greater its total electrical resistance. The conductor's resistance and the amount of power flowing through it determines how much heat the conductor generates. The equation looks like this:
Power = I2 * R
Power is the amount of energy lost due to resistance. The letter I represents the amount of current flowing through the conductor. And R stands in for the conductor's resistance. Increase the current or the resistance of the conductor and you get more power lost as a result -- that means more heat.
So let's say you've got a conductor that generates heat sufficient enough to increase the temperature of several liters of water from room temperature to around 140 degrees Fahrenheit (60 Celsius). That conductor may need to be several feet long to generate enough heat at a safe level of power. By coiling the conductor, you can have enough length without taking up too much space. That's why you'll find heating coils in devices like toasters or space heaters.
When you set an immersion circulator to a particular temperature, the control circuits will direct an appropriate level of current to the heating coils. As the coils heat up, they transfer heat to the surrounding water. The pump in the circulator causes water to flow through the coils, creating a more even heating environment. As the temperature of the water nears the target temperature, the control circuits can direct less current to the coils. Since joule heating depends upon resistance and current, decreasing the amount of current flowing through the heating element generates less heat.