Necessary Roughness

I remember a discussion in my Physical Chemistry II class at the then University of Missouri-Rolla (now MST). Dr. D. Vincent Roach had just finished a day and a half derivation of the ideal gas law from statistical mechanics — he went into a little more detail than Wikipedia. You may remember the final line of the derivation from high school chemistry class:

One student, probably one of the most brilliant minds of our Chemical Engineering class (seriously, no sarcasm), tried to get the good doctor’s attention, first by raising his hand, then gently “ahem”-ing, and then surprising the class with a very rude snap of the fingers.

Finishing his proof about 5 minutes later, Dr. Roach turned to the class to take questions. The student asked, “Why not just use Redlich-Kwong?”

Dr. Roach was for the first and only time that year flummoxed and annoyed. He full-well knew what the Redlich-Kwong equations of state were, but the conversation was in his view irrelevant. It was like asking someone teaching basic multiplication, “Why not just use exponents and logarithms?”

But the student persisted. Redlich-Kwong was way superior. It gave better results. It accounted for different materials. Why did we waste a day and a half with the derivation of an inferior gas law?

The kindly old man kept his smiling poker face, but his voice betrayed his anger at the insolent one. He dismissed the entire class right then and there, only 20 minutes in. Most of the class thought it was cool, but I thought it was a missed opportunity. The problem lay within how each method was generated.

The first method, the ideal gas law, was first derived in 1834. It used very few assumptions and some rigorous mathematics to predict how gases would behave under certain conditions. If it were to prove somehow false (which it is, for very high and very low pressures and temperatures), then the fault wasn’t in the measurements, but in the assumptions. A deviance from the “ideal” was an opportunity for discovery.

The second method, published 125 years later, used coefficients (fudge factors) to model the behavior of a gas under a wider spread of circumstances. If the equation didn’t match the actual behavior, the constants could be adjusted, potentially covering up new opportunities for discovery.

But I think the great Dr. Roach, still on the MST faculty list, may have found most offensive, beyond the student’s behavior, the desire to get to the “right answer” without appreciating what it took to get there.