Comment: When a metal is heated, there is current (ie flow of e) flowing too

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Heating a metal causes electrons to transfer energy, leading to a flow of electrons, which can be interpreted as current. However, while electrons move, they typically do so in both directions, resulting in no net current. The temperature of a solid relates more to the lattice vibrations (phonons) than to electron movement. The thermoelectric effect, specifically the Seebeck effect, occurs at the junction of two different metals rather than within a single metal. Understanding these principles is crucial for practical applications like thermocouples.
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Comment: "When a metal is heated, there is current (ie flow of e) flowing too"

"We all know that metals are good conductors of heat. When one end of the metal is heated, the electrons will rapidly transfer the energy to the other end. This energy transfer often involves the flow of electrons from one end of the metal bar to the other. And since we know current is the rate of flow of electrons, the fact that there IS a flow of electrons (in the conduction process) means that current is actually flowing in the bar."

Any comments for the above paragraph?
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Its called the thermoelectric effect. Its make for a lovely practical. Join a piece of copper and constantan wire together and immerse in a ice bath, room temperature and then a water bath and various temperatures up to 100 Celsius. Use a current balance to determine the e.m.f provided at the various temperatures and you have a callibrated thermocouple. Neat.
 


The fact that electrons are involved in heat conduction in metals does not mean that there is a current flowing, simply because there will -on average- be the same number of electrons moving in both directions.
Also, when we talk about the temperture of a solid we are effectivly referring to the temperature of the lattice (i.e phonons); not the electrons. In a real metal the electrons are scattered so often that they never actually travel in any particular direction for very long; there is a constant exchange of energy with the lattice.
Remember that if there were no electron-phonon scattering the metal wouldn't get hot at all (in the conventional sense).

(if the scattering rate is low enough it is actually possible to create a situation where the temperature of the electrons is significantly higher than the temperature of the lattice).

The thermoelectic effect is different, because it involves TWO metals; the effective "device" is actually the junction between them, no the individual metals.
 


Its called 'THE SEEBECK EFFECT'
SCIENTIST SEEBECK have observed this first of all!
 
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