Technical Principles

That Ugly Third Term


Chemists and Chemical Engineers, you may smile inwardly as you read this, but I am addressing my Mechanical Engineering colleagues who, like myself, learned in thermodynamics class that U, the internal energy of a system, is comprised of three terms and then forgot all about one of them. It’s easy to do when the systems we work with – heat engines, steam boilers, refrigeration etc. – deal only with the interplay of thermal energy (the TS term) and mechanical work (the PV term). That ugly looking third term, chemical energy, had little relevance to my world.

Some systems inhabit a realm too broad to fit that mindset, and and my study of Pass-through distillation has forced me to change my point of view. I have come to appreciate the power and importance of chemical energy, and that change can be compared to leaving Flatland and entering the real three dimensional world. Everything interesting in the universe, with exception of a few coarse industrial processes, hinges on that third term.

Pass-through distillation cannot be understood without accepting the counter-intuitive truth that a warm liquid can absorb a cool gas. This phenomenon, closely linked to boiling point elevation, is at the very root of how PTD operates.

1 thought on “That Ugly Third Term”

  1. The chemical potential term is the same as saying: the partial derivative of Gibbs energy with respect to the number of moles of one species, when temperature, pressure and all OTHER species are held constant!!!

    And dG = -SdT + VdP

    So the three term definition of U is a natural function of (S,V,T,and P) when chemical potential is involved, but only S,V when not included.

    Took some thermo and multi-variable calculus for me to see this.

    Hope you get this comment.

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