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In my University physics class [first year engineering student] I learned that

"for a capacitor in a vacuum, capacitance $C$ depends only on the shapes, dimensions, and separations of the conductors that make up the capacitors".

Does this mean that the vacuum makes material properties null.

This statement, which, with my current knowledge of physics I do not believe in, due the questions I have specifically relating to material and temperature which I thought would have been important. I wanted to focus on temperature first with my questions, so I was wondering the following:

Given a capacitor in a vacuum what would happen at extreme low temperatures and high temperatures?

And how would this differ from what would happen not under a vacuum, how would pressure affect capacitance.

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  • $\begingroup$ Are you considering a capacitor with vacuum as the insulator or some other dielectric? $\endgroup$
    – Puk
    Feb 21 at 3:58
  • $\begingroup$ With the vacuum as the insulator. Thank you. Would the answer change if it was a dielectric, if so what materials would result in different results on the capacitor? $\endgroup$ Feb 21 at 4:08
  • $\begingroup$ @WilliamBanquier hyperphysics.phy-astr.gsu.edu/hbase/electric/dielec.html $\endgroup$
    – ManRow
    Feb 21 at 4:14
  • $\begingroup$ @WilliamBanquier Yes, dielectric constant (permittivity) is a function of temperature in general. I don't know what this dependence looks like for specific materials, but a key term is "temperature coefficient of capacitance" if you want to delve deeper into that. $\endgroup$
    – Puk
    Feb 21 at 4:16
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Feb 21 at 4:17

2 Answers 2

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If the conductors are surrounded by vacuum, with no dielectric material in between, the only temperature we are talking about is those of the conductors. As temperature increases, the conductors will normally expand, altering the capacitor geometry, and hence the capacitance. If the conductors are somehow prevented from expanding, you are then necessarily imparting pressure on the conductors, although I don't know why that would affect capacitance.

As naturallyInconsistent has mentioned, thermionic emission of electrons from the conductors can take place at elevated temperatures, resulting in a "leaky" capacitor, effectively a capacitance in parallel with a resistance.

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The extreme low temperature limit is perfectly fine and nothing changes. In fact, what the professor or textbook is trying to say, is that for a rather wide range of temperatures, up to a few hundred degrees Celsius, there is basically nothing that will change. It is when you go above a thousand degrees Celsius that, at some point the capacitor plates would either melt or start emitting electrons, in which case it basically stops behaving like capacitors at all.

If there are stuff in between the plates, they get polarised, and that changes the capacitance, often dramatically. We intuitively expect that a lot more things can change, and change due to changes that we have safely ignored in the vacuum case.

I do not think it is very healthy to doubt your professors or textbooks on a topic so mundane and so easily testable in the laboratory. There is more room for doubt if it is some obscure little thing that is difficult to experimentally check or is some mathematical nitpick. If they cannot even get such a basic thing correct, maybe you should consider changing universities.

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