# Calculating Energy and Enthalpy

We have already discussed the fact that we must use reference
states in order to get numerical values for the energy and enthalpy
(since we can not know the *actual* numbers!). This didn't
bother us since we are only interested in *differences* in
these quantities (so that the reference state that we choose
cancels out!).

We will assume that we have "ideal mixtures" in all cases! (That
means that the *total* energy or enthalpy of a mixture will
be equal to the sum of all of the component's
energy/enthalpy.)

NOTE

This is not strictly true! In fact, it is only a
good approximation for gas mixtures or mixtures of similar liquids.
We will not get a chance to talk about energy/enthalpy of mixing,
but it is a simple way to alleviate our assumption.

### Fictitious Paths

Since we know that the Energy depends on:

- Temperature
- State of Aggregation (phase)
- Chemical Composition

and we know that H = U + PV, then H depends on all of these as
well as P.

So, there are four things ($\Delta T$, $\Delta P$, phase
change, rxn) that may cause a change in energy or enthalpy.

NOTE

You are already familiar with the "heat" (change in
enthalpy) involved in changing the state of aggregation (Latent
Heat of vaporization, for example)

We will talk ahout changes in chemical composition in a few
lectures.

We need to deal with changes in T and P

So in order to calculate enthalpies or energies, we need to
determine the *changes* that occur as we move fromour
(required!) reference state to our actual state.

Let's consider a simple example:

Is there a reason we should choose one of these paths over the
other?

NOTE

When we calculate energies or enthalpies we need to
choose a path (perhaps ficticious, but whichever is easiest!) that
represents the changes that the substance undergoes.

Our ideal fictitious path can be decomposed into the smallest
number of steps that are each of 1 of the following several types:
a change in T (at constant P and constant phase), a change in P (at
constant T and constant phase), and phase changes (again, we will
consider reactions later).

OUTCOME:

Generate "fictitious paths" from your reference
state to your desired state

TEST YOURSELF

Develop a path for calculating the enthalpy of
steam at 200C and 1.5atm relative to a reference state of ice at
-10C and 1 atm. How about internal energy?