# Single Phase Systems

In (almost) all of the problems that we have discussed, you were given all the information that you needed. Obviously, in real life, you will be required to get all the information you need by yourself.

This information can come from:

Measured Data from an existing process (experiments!)
Process Specifications/Design
Physical Properties/Laws

(Obviously, you are also limited by physical constraints and must not violate balances of mass or energy.)

Just like we were sometimes given process specifications to be used in our degree-of-freedom analysis, we will also use physical laws as additional relations to lower the number of degrees-of-freedom.

##### NOTE

We have already seen how to use measurements (calibration curves) to determine the composition and density of a process stream

## Liquid and Solid Densities

Most Liquids and Solids $\rightarrow$ density decreases with heating, and density increases with pressure.

NOT VERY MUCH $\rightarrow$ "incompressible"!

##### NOTE

Because solids and liquids are essentially incompressible you can use the density at one T and P for almost any other T and P.

Mixtures are difficult, but usually assume either:

##### DEFINITION

For mixtures of "similar" solid or liquid materials (e.g., ethanol and methanol) the density of a mixture may be approximated by averaging the specific volumes. This is termed assuming volume additivity.

SIMILAR: $\rho_{average} = \frac{1}{\hat V_{average}} = \frac{1}{\sum x_i\hat V_i}$

##### DEFINITION

Another method of approximating the density of a solid or liquid mixture is to average the densities.

OTHERWISE: $\rho_{average} = \sum x_i\rho_i$

##### Outcome:

Determine the density of a mixture of liquids.