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The textbook I am currently reading Thermodynamics: An Engineering Approach by Cengel & Boles classifies the energy transferred to a system by an electric heating element as a work interaction instead of a heat transfer interaction.

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I have searched for what exactly qualifies as work in thermodynamics and the most satisfying answer that I've found (here) is that an energy transfer is considered a work interaction if it involves a uniform change in the energies of all of the particles of a system by the same amount without changing the shape of the energy distribution of the particles in the system. However, the heating of a system through an electric heating element obviously changes the energy distribution of the particles inside the system as it changes the system's temperature. So why is the heating of a system through the use of an electric heating element considered a work interaction and not a heat transfer?

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If you include the heating element is part of your system, then the electrical setup supplying the electrical energy to your system is doing work on your system. If you include the heating element as part of the surroundings, then there is heat being transferred to your system by this part of the surroundings. So it all depends on whether you include the heating element as part of the system or part of the surroundings. In your book's example, the heating element is treated as part of the system.

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  • $\begingroup$ Thanks for the answer. So then would the work done by the surroundings (battery)on the system just be the work done by the electric field set up by the battery on the charges inside the wire of the heating element? $\endgroup$ Sep 13, 2021 at 2:36
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    $\begingroup$ If you are asking whether it would be the voltage times the current times the time, then yes. $\endgroup$ Sep 13, 2021 at 12:39
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I think that you have found that the question what exactly qualifies as work in thermodynamics? cannot easily be answered in one sentence. A way forward is perhaps to start by considering the terms in the first law of thermodynamics for a system which does not change in composition and to consider work as a process to do with energy transfer.

There is an internal energy term and then there is a heat transfer term which is energy transferred between a system and its surrounding because of a difference in temperature which importantly is a one way process in that the transfer is always from the higher temperature to the lower temperature.
In your diagram that would be the water (surroundings) having heat transferred from the tank (system) to the water.

You now look as the other ways of transferring of energy in and out of the system and call that work and this is where it becomes tricky but not for all examples.
Perhaps the simplest is the change in volume of a system by the application of external forces when mechanical work is done.
What is not so obvious is how to categorise the effect of the electric heater and to do that you need to decide as to whether the heater is part of the system or the surroundings.
If the electrical heater is part of the surroundings then the transfer between the heater and the system is via heat but doing that makes calculations difficult.
If the heater is part of the system then the transfer to the system would be characterised as work as per the falling weight definition with the falling weight doing work turning a generator which produces "electricity" which in turn increases the internal energy of the system.

I know that I have not told you which of the "one sentence" definitions of work I favour but I do suggest that you consider other examples eg temperature of the water in waterfall, infra-red radiation interacting with a system, etc and see if you can exclude heat transfer and then how it might be considered as work via the falling weight definition or the energy distribution definition that you have mentioned in your post or . . . . .

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  • $\begingroup$ Thanks for the answer. When you say "if heater is part of the system, then the transfer to the system would be characterised as work", is that because you can think of the electric field set up by the battery (which is part of the surroundings) as doing work on the electrons inside the heater (which we have chosen to be part of the system)? I suppose this work would indeed be easy to calculate since the voltage of a battery is literally the work done on a unit charge as it loops through the circuit. $\endgroup$ Sep 9, 2021 at 9:41
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As Farcher and Chet Miller explain, if the heater is part of the system, then we do (electrical) work on the heater and therefore supply work to the system. We are supplying this energy even if the system is perfectly thermally insulated and cannot receive heat.

In this case, though, the heat/work distinction is rather legalistic. This is because the work we supply is wholly irreversible, unlike the wholly reversible work that we would perform on the system by slowly pushing in a frictionless piston. It is reversible work that "involves a uniform change in the energies of all of the particles of a system by the same amount without changing the shape of the energy distribution of the particles in the system". But with wholly irreversible work you might as well be supplying heat – you alter the distribution of energy among the different energy levels of the system, rather than altering the energy levels themselves. And the heater might as well be outside the system supplying heat to the system$^*$ as inside the system having (electric) work supplied to it from outside!

$^*$ which, for strict comparability, ought now to include an unconnected electric heater

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So why is the heating of a system through the use of an electric heating element considered a work interaction and not a heat transfer?

You need to distinguish between energy transfer between the electric current and a material which raises the temperature of the material (work transfer), and the energy transfer between the material whose temperature is elevated by the current to its lower temperature environment (heat transfer).

Heat is defined as energy transfer due solely to temperature difference. The raising of the temperature of a material by electric current is not due to a temperature difference between the current and the temperature of the material. At the microscopic level it is the transfer of the organized kinetic energy (KE) associated with the flow the electrons (drift current) to the molecules of the material by collisions.

Electrons alternately lose kinetic energy in the collisions and regain KE from work done by the electric field. So in effect, the work done by the electric field to maintain the drift current transfers energy to the molecules of the material. Those collisions in turn increase the average random KE of the individual molecules resulting in an increase in the material temperature. The increase in the material temperature above the temperature of its environment results in energy transfer to the environment in the form of heat. Thus the term Joule heating refers to the consequences of electrical work. Similarly, friction heating refers to the consequences of energy transfer by friction work, which occurs when one rubs one's hands together raising the temperature of the skin.

By contrast, energy transfer by heat conduction from a material of higher temperature (higher average random molecular KE) to a material of lower temperature (lower average random molecular KE) is due to collisions between the random (disorganized) motion of the molecules of the higher temperature material and the random motion of the molecules of the lower temperature material.

Hope this helps.

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