We hate teaching by formula, so this question gives us a chance to get a little beyond that approach.
"Elecrtical E = QV"
This formula as it stands refers to the energy gained or lost by transporting a charge Q from one place to another where the difference in the voltages is V. For example, if a charge Q flows from one terminal of a battery to another, then QV is the energy delivered (say, to a light bulb) and taken away from the battery when this happens. You can add energy to rechargeable batteries (don't try this with non-rechargeable batteries) by forcing charge to flow in the other direction. This formula assumes that the voltage difference remains constant. The energy stored in a capacitor has a similar form, E=QV/2. The difference here is that the voltage of a capacitor changes as you add charge to it, and you have to add up all the contributions V*dQ for each little bit of charge dQ you put on the capacitor, where Q=CV is the expression which gives the voltage as a function of how much charge is on the capacitor. The capacitor relationship also appears as E=CV^2/2.
"Kinetic E = half mv squared"
0.5*m*v^2 is the kinetic energy of a mass m that's moving at speed v, so long as v is much less than the speed of light. The formula is not correct for things moving close to the speed of light.
"nuclear E = mc squared"
ALL energy is equal to mc^2, where m is inertial mass (not the rest mass) and c is the speed of light. That has nothing special to do with nuclear energy. It gets used more for nuclear problems because they involve large enough energy changes to make a noticeable fractional change in m.
"Gravitational Potential =m.g.h"
That's ok for a mass m close to the surface of the Earth, where the gravitational acceleration is g. It doesn't work as the mass gets farther away.
"but i can't get:
Radiant thermal E =
Elastic Potential E =
Light E =
Sound E (dencity) =
Thermal E ="
Here the mathematical expressions that are useful depend on what you know about the situation. For example, you can give electromagnetic energies (including light) in terms of the integral over space of the sum of the squares of the electrical and magnetic fields, if those are what you happen to know. Or if you know the temperature, you can give the electromagnetic energy density in terms of the absolute temperature, T. It's proportional to T^4.)
If you asked 'How much thermal radiation energy is present in a meter^3 box at room temperature?", we could answer that. We could tell you how the answer depended on volume and on T. We cannot answer "What is the formulae for thermal radiation energy?" because we do not know what sort of information you have to start.
The categories you give are all mushed up and overlapping. "Thermal energy" INCLUDES "radiant thermal energy". "Light E" and "Sound E" sometimes are thermal and sometimes aren't. "Elastic potential" often goes as the square of how much something is stretched or compressed from its equilibrium position. It's also often thermal, and it's part of the sound energy in solids and liquids.
So please, try to think of these things in terms of real physical questions, not just a bunch of names and formulae. Tell your teachers that we said so.
(published on 10/22/2007)