capacitor COE question

Fun! Sure why not. But could you measure it? Assume the heat capacity of the cap is about 1 J/(gram-K) What's the Q^2/C energy change? (for 0.1uF and 10 V looks like only ~10uJ's of total energy)

George H.

.highlandtechnology.com  jlarkin at highlandtechnology dot com

Yes, the heat capacity is going to depend on the charge. Can't be otherwise.

Why should C*V be constant? w.

That does not compute. If the capacitance changes, and the charge does not, the voltage must change inversely, keeping the stored electrical energy constant.

Yeah, I thought so. But as George says, it wouldn't be easily measurable for a real capacitor.

Thinking about this, for no good reason, I tripped across this site:

No, OP was right, and it's a cute question. Stored energy is proportional to C and V^2, so even if V is inversely proportional to C, then the energy will change.

A simpler way of putting it is that CV=Q will be constant (if the capacitor is isolated) and the energy is proportional to Q^2/C, which obviously changes.

0.5 farad, 2 volts, 1 joule.

Same charge, different energies.

Assuming no leakage, Q should be constant.

Ok, I see it now.

Specific heat and thermal conductivity start to do really "interesting" things at very low temperatures.

Yes, the charges are now further apart due to thermal expansion. Moving them further apart added some energy.

Probably.

In (say) a parallel plate air-gap capacitor, the plates will bend towards each other slightly as charge is added. Is the electrical energy stored the same as the mechanical energy which would be required to bend the uncharged plates by the same amount?

Cheers

Yup. Work has to be done on the stored charge, just as you say. Of course it might not be exactly V*delta_C as you'd expect, because the voltage coefficient might change with temperature too, and the energy is actually the integral of CV*dV.

Cheers

Phil Hobbs

Phase transitions do make life more interesting, but as the article says, in the temperature vs internal energy curve, it's just a flat spot and not a big fat discontinuity. That would be pretty simple to model in SPICE, I should think--just a constant times a Boolean added to the charge on a capacitor, or something like that.

The same issue exists in thermal conduction, but is much more serious, especially at low temperature--the Lakeshore Cryogenics catalogue has tables of "Thermal conductivity integral" because you won't get anything like the right answer otherwise.

Cheers

Phil Hobbs

.highlandtechnology.com  jlarkin at highlandtechnology dot com

Ouuu I like that graph! (figure 1.) I'll have to order some poly- propelene and poly-ethylene. I wonder what the phase change is? Maybe the dielectric constant changes too?

The interesting (physics-wise) way to compare materials is by the molar heat capacity. (Water is amazing in that regard.)

George H.

Glass transition point. Teflon's is exciting too--the CTE changes by like a factor of 10. There are some cool graphs here:

Modelling the thermal energy looks like a good application for one of JT's fave tanh functions.

Cheers

Phil Hobbs

Yep. Distraction.

Wanted to point to the "capacitor paradoxon" when an uncharged cap is switched parallel to a charged cap. But you know anyway.

w.

If the plates were perfectly rigid, you'd still store the electrical energy.

If you pull the plates of a vacuum pp capacitor apart, you do work on it, like stretching a spring. CV is conserved, but C goes down and V goes up, so the work you did pulling the plates farther apart is stored as electrical energy, 0.5*C*V^2. Like a spring, you can get that mechanical energy back later.

Unfortunately, the temperature coefficient of vacuum is zero (I think!) so it's not a useful analogy to illustrate my case.

Works in fluids--long long ago an old friend of mine, Sam Batchelder, built what he called "capacitive muscle", using oil inside bags made of flex circuit material, using that effect. (When it's the material that moves, its fancy name is "dielectrophoresis".)

Cheers

Phil Hobbs

No such thing as perfect - if the spring is stiffer, it just moves less for the same force.

Cheers