# (148e) Liquid/Vapor Equilibrium Via Equations of State for First Semester Sophomore Students

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Missouri S&T

The availability of powerful computers and  of “ready to use” software for the estimation of thermodynamic properties of pure components or mixtures have transformed some basic thermodynamic courses.   Many textbooks come with software already developed or with enough information for the students to write simple programs.   Are we forgetting concepts by emphasizing calculations?  An affirmative answer to this question will definitely weaken the quality of our programs.  It is obvious that some compromise is needed between the teaching of concepts and the temptation of overusing computers.

I started to include more and more complex (computer based)  calculations in the two thermodynamic classes that I teach as the accessibility of computers increased (I have been doing this for 20 years).  Soon I realized that many of the homework problems were not didactic all because the students were becoming just  “calculating machines”.  The fast pace of homework assignments left little room to explore conceptual issues.      A few years ago I started with the idea of “mini project” in which the students must use an equation of state to generate a table of thermodynamic properties for a particular compound.

They use an equation of state that I select from the open literature (we use from 6 to 10 different E.O.S. each semester but no two groups have exactly the same problem because they use different compounds).  They have to derive expressions for enthalpy and entropies for that particular equation of state and use those values to find the saturation pressure for a given temperature.  In addition they have to generate H-S, and P-V plots and compare their calculations against experimental data that they have to find too (an excellent tool to increase the national membership).   The parameters of the equation of state are not explicitly given but some references are made available.

Some specific tasks are: 1) Derivation of  the expressions for enthalpies and entropies for the  equation of state.  This is done by hand and they have to check their solution using Maple.  2) Solving  the cubic equation of state for a particular temperature (sub-critical) at various pressures.  3) Determining the position of the spinodal and binodal curves by finding  points of divergence of the isothermal compressibility and by finding the pressure at which the condition of chemical equilibrium is satisfied.  4) Preparing the required plots and including experimental values.

The “project” has become a staple for the  Thermo 1 course and to a lesser extent of  Thermo 2.   We have incorporated this into our ABET strategy.   The work done by the students is used as a performance indicator for the program outcome:   “The S&T Chemical Engineering program graduate will have an ability to apply knowledge of mathematics, science, and engineering fundamentals”.

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