# 07.07 Implications of Real Fluid Behavior

### PREOS Derivatives:(dU/dV) and (dCv/dV) (3min)

Derivative Relations for the Peng-Robinson EOS (3:18) (msu.edu)
The derivatives (∂U/∂V)T and (∂CV/∂V)T are evaluated for the Peng-Robinson EOS and the concept of expressing non-measurable properties in terms of measurable properties is discussed.

Comprehension Questions:

1. What derivative do we need to use when developing formulas for departure functions in Chapter 8?

### PREOS Preview

Sneak peek: the properties you need from an equation of state. Perhaps the most important implication of real fluid behavior is that the properties we need are influenced by the equation of state. Making the connection from P(V,T) to U,H,S is a lonnnggg story starting with derivative relations, what equations of state are and where they come from, and finally combining the derivative relations with the equation of state to formulate the corrections to the ideal gas law that enable us to get properties. In the end, the final conclusion of this story is a relatively simple and useful tool called PREOS.xlsx. Maybe it will help you to sneak a peek at the final conclusion before you get too bogged down with all the derivations.

Comprehension Questions:

1. Benzene is heated from a saturated liquid at 1 bar to a compressed vapor at 500K and 20 bars. Compute the change in enthalpy (J/mol) and entropy (J/mol-K).

2. CO2 is to be used as the working fluid in a modified Rankine cycle. CO2 is (a) heated from 73C to 140C at 320bars. Then it is (b) expanded isentropically to 80 bars. Then it is (c) cooled to 30C, 80 bars and (d) compressed isentropically to 320 bars. Assume the PREOS thermo model.
(a) Solve for the QH (J/mol) of step a.
(b) Solve for the Ws (J/mol) of step b.
(c) Solve for the Qc (J/mol) of step c.
(d) Solve for the Ws (J/mol) of step d.
(e) Solve for the thermal efficiency of this process and compare to the Carnot efficiency.