February 15, 2012  Tagged with:  Comments Off on Useful Definitions and Identities for Thermodynamic Potentials

This is just a summary of many of the definitions and identities I find useful when working with the basic thermodynamics of a system or process.  It is not meant to be a comprehensive list.

# Mathematical Identities

Using the reasoning behind the notation used for derivatives of thermodynamic potentials, there are some useful identities given the following prototypical system

Eq. 1) $\displaystyle X=X\left(Y,Z\right)$

This equation represents a generic thermodynamic potential of an arbitrary system or process as a function of two implicitly extensive thermodynamic potentials.  Adopting the notation

Eq. 2) $\displaystyle\underline{X}=\frac{X}{N}$

To denote the relationship between intensive variables, extensive variables, and the size of the system allows for the trivial conversion between system size dependent and system size agnostic thermodynamic relationships.  The total differential for the extensive form of the thermodynamic potential for the prototypical system is given by

February 14, 2012  Tagged with: , ,

When I took my process thermodynamics course as an undergraduate student, I was told to use what I had initially considered to be a completely redundant notation for partial derivatives for thermodynamic potentials.  The notation involved wrapping the partial derivative in a set of parentheses and noting which variables were “held constant” as a subscript.

Ex. $\displaystyle\left(\frac{\partial P}{\partial V}\right)_{T,\vec{N}}$

The derivation leading to this was woefully devoid of the mathematical basis for this apparently redundant notation.  Furthermore, so was the general literature on the subject, most of which consisted of fleeting introductions to their respective application.  As I played with the idea, it became clear why this notation was indeed very necessary.  It was only as I was solving a separate problem on my own that such notation yielded valuable information about the nature of the potentials being described.

January 16, 2012  Comments Off on Old Work to be Posted Over the Next Few Months Over the next few months I will be posting about many of the independent projects and research projects I did as an undergraduate.  They range from metabolic models to full process designs and cover a diverse selection of chemical engineering principles, several with significant real world applications.  Starting things off will be a walk through of a proof I wrote in response to a test grade I did not agree with and how the results of the proof may be used both to simplify and enhance a graphical method for predicting distillation column behavior.  This proof will be the basis for a paper I will be writing on the subject as well.

December 9, 2011  Tagged with: , , , , , , ,  Comments Off on Study of Light Paths in a Fluorescent Medium

This time I used a bottle of tonic water with my 405nm laser.  The quinine in the tonic water is fluorescent and glows with a bright blue color under UV light.  It also clearly displays where the light path is.