First of all sorry about my english it's not my mother tongue.
Problem statement:
A cylindrical capacitor is placed in the sea so that when a wave comes (the water goes up), the water becomes the capacitors dielectric, when the wave has passed (the water goes down) the air becomes the dielectric.
So now when the water is at its highest, i attach a battery to the capacitor.
When the water goes down i detach the capacitor from the battery, this creates an isolated system in which the charge remains constant and can change the potential difference between the capacitors plates.
The force of gravity makes the water that was between the capacitors plates go down, and so it reduces the capacitors capacitance. The dielectric constant of water is quite high (about 81) and the change of capacitance is also quite high.
The charge remained the same but the potential difference between the capacitors plates has increased.
This means that the energy in the system has increased.
So i found a way to harvest energy from the waves movement without moving bodies…. but….
- Explain why this system in practice can not really work.
- Think about how to make it work (even if with reduced performance, how to make the capacitor stay at the same height is not to be considered).
- Estimate how much energy could be made out of such a device.
The attempt at a solution
I think this does not work because sea water is not distilled which means it conducts current. So now there's a current flowing through the capacitors plates which i think would damage the capacitor itself.
Or maybe the battery would get damaged because the capacitor with sea water inside makes a short circuit?
To make it work i think one would need to put distilled water in the capacitor or another insulating material and make it go up and down the capacitor thanks to the waves movement.
I have absolutely no idea how to estimate how much energy could be made out of such a device.
If i'm not mistaken energy in a cylindrical capacitor is calculated as:
$$U = \frac{1}{2}C\Delta V^2$$
So i thought about calculating
Uw = energy when the capacitor is filled with water
and then
Ua = energy when the capacitor is filled with air
and then doing
Uw-Ua = energy generated by the device
But i'm not sure this is right.
What do you think?
Best Answer
Yes, you can convert wave energy to electrical energy in this manner (but it's horribly inefficient — there are much better ways to extract energy from waves).
Two equations cover what you're proposing. The first is the relationship between charge, capacitance and voltage:
$$Q = C \cdot V$$
The second is the relationship between energy, capacitance and voltage:
$$E = \frac{1}{2}C \cdot V^2$$
Start by putting a charge on a capacitor that's filled with water, and then removing the water. The first equation tells us that if the capacitance goes down by a factor of 81, then the voltage must go up by the same factor, because at this point, the charge can't go anywhere.
But the second equation says that if the capacitor had a certain amount of energy with the water in it, afterward, it has 81 times as much! Capacitance went down by a factor of 81, but \$V^2\$ went up by a factor of 812. E must rise by a factor of 81 in order to keep the equation balanced.
Where did this energy come from? It takes physical work to remove a dielectric from a charged capacitor. In this case, the potential energy of the mass of water within the capacitor was reduced when gravity pulled it out during the low part of the wave. And when the next peak comes along, the energy in the wave pushes the water back up against gravity.
When you put real, physical numbers on the values for C and V that you can realistically work with, you'll soon realize that the power (energy per time) that you can extract is miniscule.