Energy Balance Procedure

Before we actually outline the general procedure for doing energy balances, we first need to talk a little more about the internal energy and enthalpy and how we can obtain values for them.

The first thing to mention is actually quite simple. If we want to calculate or look-up values for the internal energy or enthalpy, would it be easier to use extensive versions of the variables or intensive?

State Variables and Reference States

If I asked you to tell me the specific enthalpy (internal energy) of the final material in each of the two examples below, would they differ? would you need more information?

If we use specific energy and enthalpy, the value depends only on the (thermodynamic) state of the system, not on the path of how you got there. This is important for anumber of reasons, as we will see...

DEFINITION

State Functions depend only on the thermodynamic state of the system (T, P, phase). (Remember Gibbs Phase Rule tells vou whether the thermodynamic state of the system is fixed or not)

So, now we know that as long as we know "where we are" in the state of the material, we know that the energy and enthalpy are fixed values, but what are those values?!

This is a trick question. It is, in fact, impossible to measure the energy or enthalpy exactly, but it is easy to measure CHANGES in the energy or enthalpy (as you can see from the energy balance equation: hold kinetic and potential energy fixed, apply no work, and add a known amount of heat).

OBJECTIVES:

Explain why one must choose a reference point

So if we don't know the actual value, but only differences, what do we do?!

Since we are doing balances, we are really only interested in differences of differences! Just like in the case of changing a temperature difference from Celsius to Kelvin, where the offset (reference state!) was canceled out, here we can choose things such that the reference state chosen is immaterial! To get the change in enthalpy in a balance, we define BOTH enethalpies relative to the same reference state and then that reference state CANCELS OUT!

(H₁ - H_ref) - (H₂ - H_ref) = H₁ - H₂

In all of our dealings with these state variables (energy and enthalpy), we will use a reference state (set equal to zero) in order to do the calculation).

NOTE

As we will see in our next lecture, when we choose a reference state, we can set the enthalpy (energy) of that reference to any arbitrary value. For simplicity, we will set these arbitrary values to zero.

Procedure

Typically, these new problems will (again) look very much like the old ones. We will only now be asked to calculate the amount of heat or work going to/from the system.

The procedure will look like this...

• (TRY TO) Perform all material balances (doing degrees of freedom and all the rest of that procedure)...it's possible that you will have to count the energy balance as an additional equation in your MASS degrees of freedom analysis (of course, you must then also count the unknown from the energy equation in this analysis)
• Write down the appropriate energy balance equation (closed or open)
• Choose a reference state for all the species in the process (T, P, phase)
• Simplify the balance equation (see the last lecture for explanations of simplifying each term)
• Obtain values for all the specific energies (U) or enthalpies (H) and calculate the changes in these values (remeber to add in all the ins (initials) for each species and all the outs (finals) for each species!).
• Calculate any (other) terms that didn't drop out (kinetic or potential)
• Solve for the unknown thing!

OBJECTIVES:

Simplify and solve the General Energy Balance for non-reactive systems

TEST YOURSELF

Let's look at a simple example!