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|08.07 - Implementation of Departure Functions||Click here.||20||1||
Helmholtz Example - vdW EOS (uakron.edu, 18min) This video begins with a brief review of the connection of the Helmholtz departure with all other departures then shows four sample derivations assuming that Z is given by the vdW EOS: (1) the Helmholtz departure , (2) the internal energy departure from the Helmholtz departure. (3) the Helmholtz energy from the internal energy (4) the Z factor from the Helmholtz departure. The procedures illustrated here can be applied to any EOS starting with any part (U, A, or Z) as given to derive any other departure: ZUHAGS.
|08.07 - Implementation of Departure Functions||Click here.||20||2||
Helmholtz Energy - Mother of All Departure Functions. (uakron.edu, 10min) This screencast begins with a brief perspective on energy and free energy as they relate to concepts from Chapter 1 and through to the end of the course. Then it focuses on how the Helmholtz departure function is one of the most powerful due to the relations that can be developed from it. The Helmholtz departure is relatively easy to develop from a density integral of the compressibility factor. Then the internal energy departure can be derived from a temperature derivative. Alternatively, if the internal energy departure is given, the Helmholtz energy can be inferred by integration, and the compressibility factor can be derived from a density derivative.
|09.10 - Saturation Conditions from an Equation of State||Click here.||20||1||
Solving for the saturation pressure using PREOS.xls simply involves setting the temperature and guessing pressure until the fugacities in vapor and liquid are equal. (5min, learncheme.com) It is not shown, but it would also be easy to set the pressure and guess temperature until the fugacities were equal in order to solve for saturation temperature. One added suggestion would be to type in the shortcut vapor pressure (SCVP) equation to give an initial estimate of the pressure. Rearranging the SCVP can also give an initial guess for Tsat when given P. This presentation illustrates a sample calculation for toluene to explore when the vapor is the stable, when the liquid is the stable phase, and when the phases are roughly in equilibrium.
1. Estimate the vapor pressure (MPa) of n-pentane at 450K according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?
|07.08 Matching The Critical Point||Click here.||20||1||
Visualizing the vdW EOS (uakron.edu, 16min) Building on solving for density, describes plotting dimensionless isotherms of the vdW EOS for methane at 5 temperatures, two subcritical, two supercritical, and one at the critical condition. From these isotherms in dimensionless form, it is possible to identify the critical point as the location of the inflection point where the temperature first exits the 3-root region. This method can be adapted to any equation of state, whether it is cubic or not. The illustration was adapted from a sample test problem. This screencast also addresses the meaning of the region where the pressure goes negative, with a (possibly disturbing) story about a blood-sucking octopus.
1. What are the dimensions of the quantity (bP/RT)?
|05.2 - The Rankine cycle||Click here.||20||1||
Rankine Example Using Steam.xls (uakron.edu, 15min) High pressure steam (254C,4.2MPa, Saturated vapor) is being considered for application in a Rankine cycle dropping the pressure to 0.1MPa; compute the Rankine efficiency. This demonstration applies the Steam.xls spreadsheet to get as many properties as possible.
1. Why does the proposed process turn out to be impractical?
2. What would you need to change in the process to make it work? Assume the high and low temperature limits are the same. Be quantitative.
3. What would be the thermal efficiency of your modified process?
|06.2 Derivative Relations||Click here.||20||1||
Assembling your derivative toolbox including the triple product rule, (uakron.edu, 13min) Beginning with the fundamental property relation, substitutions lead to Eqns. 6.4-6.7. Differentiating these and equating through exact differentials leads to Eqns. 6.29-6.32 (aka. Maxwell's Relations). Combining Maxwell's Relations with Eqns. 6.4-6.7 leads to Eqns. 6.37-6.41. With these tools in hand, and Eqn. 6.15 (aka. Triple Product Rule), you have all the tools you need to quickly transform any derivative into "expressions involving Cp, Cv, P, V, T, and their derivatives." This capability is fundamental to obtaining expressions for U, H, and S from any given equation of state for any chemical of interest. Four sample derivations are illustrated: (∂U/∂V)T, (∂T/∂S)V, (∂T/∂V)S, (∂S/∂V)A,
1. Transform the following into "expressions involving Cp, Cv, P, V, T, and their derivatives:" (∂T/∂V)S.
2. Transform the following into "expressions involving Cp, Cv, P, V, T, and their derivatives." Your expression may involve absolute values of S as long as they are not associated with any derivative. (∂T/∂U)P.
|12.05 - MOSCED and SSCED Theory||Click here.||20||1||
There are so many activity models, how can you keep them straight? This video shows how MAB, SSCED, and Scatchard-Hildebrand models are all closely related.(9min,uakron.edu) By changing the assumptions, one model can be transformed into the other. So focus on remembering one model very well, then remember the small adjustments to obtain the other models.