# Why so many energies

1. Oct 23, 2012

### mather

hello!

I come across various "energies", like free Gibbs energy, enthalpy, entropy, etc (okay, to be precise, entropic energy, enthalpic energy, internal enegry, etc)

I wonder, why all these energies?

the energy of a system stems from the movements of its components and the potential energies of its components, that's it. Am I wrong?

thanks

2. Oct 23, 2012

### HallsofIvy

Staff Emeritus
"Energy" is essentially a "bookkeepping" device. Everytime we run across a situation in which it looks like energy was not conserved, we define a new type of energy so that it is.

3. Oct 23, 2012

### AJ Bentley

Lol. that makes it sound like we have a choice in the matter. I'd substitute 'discover' for 'define'.

Ultimately, conservation of energy stems from the invariance of mechanical interactions with respect to time. It's a bit deeper than just 'Kinetic Energy plus Potential Energy'

4. Oct 23, 2012

### Nabeshin

And ultimately, because we can add arbitrary divergence terms to the lagrangian of our theory, what we get out as the noether current for time translation invariance is somewhat arbitrary.

5. Oct 23, 2012

### DrStupid

They are defined for different purposes. Let me show you an example:

The internal energy U of a system is the sum of all of its energies. According to the first law of thermodynamics its change is equal to heat and work exchanged with other systems:

dU = dq + dw

and if there is only volumetric work

dU = dq - p·dV

Now lets assume we want to measure the change of U using a calorimeter. The calorimeter measures the heat only. Therefore the volume must be kept constant to get

dU = dq

But keeping the volume constant is very difficult. In contrast keeping the pressure constant is quite easy - just by letting the atmosphere do the job. Therefore it would be useful if we would have some kind of energy whose change is equal to the heat at constant pressure. That's the origin of enthalpy:

H = U + p·V

dH = dw - p·dV + p·dV + V·dp = dw + V·dp

6. Oct 23, 2012

### Khashishi

For every combination of thermodynamic state variables, there's a corresponding free energy where these variables are held constant. Enthalpy, Gibb's free energy, and Helmholtz free energy are just some of the most common free energies, but you are free to make up your own, particularly if you are dealing with unusual state variables in your system (for example, if your system were in some kind of water level equilibrium or something).