1. Miscellaneous Contributions by:
John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO
Supported by the National Science Foundation

2. Consider the following exact differential:
Which of the following is incorrect? A. C. B. D.
ANSWER: D. E.

3. Which Maxwell relationship can be derived from the fundamental property relationship:
ANSWER: A E.

4. For this P-H diagram, which is the most likely behavior for a constant volume process at the critical volume? A B D C E P
ANSWER: D H

5. Which of these derivatives is zero for an ideal gas?1) 2) 3) 4) 5) 6)
1, 3, & 6
2, 3, & 6
2 & 6
4 & 6
5 & 6
ANSWER: C. 2 & 6.

6. As the temperature of a subcritical gas decreases, the correction term in the second virial coefficient _________.
approaches zero
becomes increasingly positive
becomes increasingly negative
ANSWER: C. becomes increasingly negative. This tests whether students realize that as the T goes down, the fluid becomes more dense relative to the ideal gas because interactions between molecules become more important.

7. Which fluid do you expect to have the largest value of the “a” variable in the van der Waals EOS?
Water
Helium
Methane
Nitrogen
ANSWER: A. Water. The “a” variable is the measure of the attraction between the particles, and water is the most polar.

8. Assume you identified three roots using the Peng-Robinson equation of state. Which of the three roots represent the physical state of the system?
The liquid root because liquids have lower U
The vapor root because vapors have higher S
The middle root
Vapor and liquid coexist
Do not have enough information
ANSWER: E. Do not have enough information.

9. Which of the following gases do you expect to have the largest value of “b” in the van der Waals EOS?
Helium
Oxygen
2,3,5‐Trimethyloctane
Water
ANSWER: C. 2,3,5‐Trimethyloctane. The largest size molecule has the greatest “b” value, which is the average volume of a particle.

10. This is an isotherm at 75°C
This is an isotherm at 75°C. There are 3 roots for the cubic EOS at 2 bar. Which is correct about these roots? x P V
fvap = fliq Z1 Z2 Z3
Psat
Fugacity
Z3 > Z2 > Z1
Z1 > Z2 > Z3
Z1 = Z2 = Z3
Z1 = Z3, but cannot say anything about Z2
Depends on the gas, no general relation
ANSWER: A. Z3 > Z2 > Z1

11. Why is the compressibility factor less than 1 at most conditions?
Attractive forces dominate
Repulsive forces dominate
Real molecules occupy volume
It is not less than 1 at most conditions
ANSWER: A. Attractive forces dominate.

12. Van der Waals accounted for the interaction of molecules
Van der Waals accounted for the interaction of molecules. Using any cubic equation of state, an increase in the parameter associated with the strength of the molecular interactions (with everything else constant) would __________ pressure.
increase
decrease
not affect
ANSWER: B. decrease pressure.

13. Comparing a radial distribution function for a square well fluid, how would g(r) change for an Leonard-Jones fluid?
The discontinuities at r = σ and r = 1.5 σ would be smoothed out
The value of g would be highest at r = 0
The value of g would go through a maximum at r = 1.5 σ
ANSWER: A. The discontinuities at r = σ and r = 1.5 σ would be smoothed out

14. The radial distribution function shown below belongs to:1 2 3 4 5 10 15
g (r)
distance (A)
An ideal gas
A supercritical fluid
A liquid
A crystalline solid
ANSWER: D A crystalline solid.

15. Which will have the highest magnitude for the enthalpy departure function at 100oC?
Water at 2.0 bar
Water at 0.5 bar
Argon at 2.0 bar
Argon at 0.5 bar
ANSWER: A. Water at 2.0 bar. Liquid will have a different enthalpy than an ideal gas.