# Capacitors & Entropy

## Main Question or Discussion Point

I was thinking of this following example:

Consider you charge a capacitor to its max with a battery, now replace the battery with a light bulb for example. The capacitor is starting to lose all the energy it had stored, is this a result due to entropy?
I mean I've learnt that an increase in entropy is a natural process, and for me, when the capacitor is losing it's energy, the system gets an increase in entropy, right? Same goes with common batteries, leave them to be (whether in use or not), and after enough time they are not usable anymore. So is it okay to see this as a result due to entropy?

Regards, Robin.

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None? :/

Entropy is defined as kln(Ω) where k is Boltzmann's constant, ln() is the natural logarithm function, and Ω is the number of different ways that a system can have particular values of whatever properties one is concerned with (i.e., the ones you are measuring).

While I imagine that the thermodynamic tendency to increase entropy could contribute the current produced when the battery is replaced, I would think that the electromagnetic forces involved would dominate under ordinary circumstances. That is, the attraction of opposite charges (the opposing surfaces in a capacitor are oppositely charged) is the main cause of the motion of the electrons.

I was thinking of this following example:

Consider you charge a capacitor to its max with a battery, now replace the battery with a light bulb for example. The capacitor is starting to lose all the energy it had stored, is this a result due to entropy?
The energy given off by the capacitor is not identical to the actual loss of energy. The actual loss of energy depends on how much energy was dissipated as resistance. Part of the resistance can be in the capacitor, and the most of the rest is dissipated in other parts of the circuit.

I mean I've learnt that an increase in entropy is a natural process, and for me, when the capacitor is losing it's energy, the system gets an increase in entropy, right?
The entropy is based on energy losses that lead to a temperature change in the system. A positive change in entropy means a loss of energy and a drop of temperature for a system. You also have an energy increase and temperature rise for another system. It's the cooling process for one system and the heating process for another, that determines the entropy.

Same goes with common batteries, leave them to be (whether in use or not), and after enough time they are not usable anymore. So is it okay to see this as a result due to entropy?

Regards, Robin.
Entropy is the result of that, not the cause of that. Entropy is a description - not a mechanism.

shpongle
It's a very good question. Thanks, I learnt a lot.

Thanks for the replies guys! I say, as the person above, I learnt a lot! There might be a few more follow-up questions from me the comin' days though!

Entropy increase happens in the resistor (light bulb in this case), not in capacitor. If you connect inductor instead, you will get an LC-tank. The energy will oscillate back and forth between inductor and capacitor. Ideal LC tank would oscillate indefinitely and the entropy would stay the same. In the real world oscillations will eventually die out and the energy will be converted into heat (with corresponding increase in entropy) due to the resistance of the wires including those in the inductor and capacitor.

Ah! That was a good "analogy", thanks again for a good answer.