# State Functions for Internal Energy and Enthalphy

1. Nov 1, 2016

### Kushwoho44

Hi,

As is commonly known,

u = u(T,v)
h = u(T,p)

I've worked with some maths proofs of this a while ago, but do you guys have an intuitive way of understanding this without the maths, that is, why the state function for internal energy is defined by intensive volume and enthalpy with pressure?

I seem to recall, I used the model for thought, that if a system had a moving boundary, as in the case of a changing enthalpy, then the volume would not stay constant, so we could not use the constant volume specific heat capacity, so we used specific pressure, but I feel like a new way of thinking about it is required for me..

2. Nov 2, 2016

### I like Serena

Hi Kushwoho44!

Enthalpy is typically used for chemical processes in an open environment, meaning that pressure is constant at standard atmospheric pressure, and volume is not easily measurable.
Internal energy is more used for physical processes where volume is measurable.

3. Nov 2, 2016

### Staff: Mentor

All of thermodynamics could be derived without ever introducing the enthalpy function. Also, an equation of state requires that f(P,v,T)=0, so that specifying any two of these determines the third. So, internal energy could also be specified as u = u (T,p). Given these facts, we must conclude that expressing u as a function of T and v, and h as a function of T and P must merely be a matter of convenience in solving various types of problems. There is nothing fundamental about it.

4. Nov 2, 2016

### Kushwoho44

Thanks guys! That makes so much sense.