Going Deeper

In high school and introductory college chemistry you're going to do a lot of problems involving the ideal gas law. It runs something like this:

PV = nRT

So simple I don't even have to typeset it. Pressure times volume equals the number of moles (n) times a particular ideal gas constant (R) times the temperature in Kelvin. It's an idealization, but a pretty good one. For your average gas at roughly room temperature and pressure it's good to within a few percent. In those intro chemistry courses, that's the end of the story. The equation says what the equation says, and that's the end of the story. Which is all well and good, unless you're a physicist.

But if you think like a physicist, you wonder why the equation is true. And I'll tell you later. Today is about why we would be interested.

The history of physics often follows a particular pattern. Someone discovers a phenomenon and manages to describe it with a purely empirical equation. No one knows exactly why the equation works, but it does. Some smart physicists think about it for a while until one of them discovers the physical principles behind the equation and shows that the equation follows from those principles. Very often those principles contain their own empirical equations which are postulated without theoretical backing and the march to deeper and deeper equations continues.

So far the march hasn't ended. It's an open question whether it ever will. The hope, however, is that eventually all the equations and principles by which the universe operates will turn out to be consequences following from one basic theory described by its fundamental equation or equations.

People have been saying that the final theory is just around the corner ever since the 1860s or so. I don't expect the people saying it today are right either. Still, I kind of hope they are. I'd love for physics to be "done" in my lifetime so I can see and appreciate the fundamental theory myself. In a larger sense though physics would not nearly be finished. In a way physics is like chess - even knowing the fundamental rules perfectly doesn't mean much in terms of understanding how to play and win. Understanding the consequences of those rules and how to use them is the real challenge.

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You placed observation before theory. Write a grant funding proposal that begins, "With no prior theoretical basis, I request a pile of folding green to discover a contradiction to published 'fact'". See how far that gets you.

In contrast, "with only untestable theory proposed - and that demanding unphysical circumstances - I request a pile of folding green to write more of it." String theory is fundable.

I admire your support for felonious negligent discovery. Theorists boast promiscuity while empiricists pay child support.

PV = nRT

I despair.... "n is the number of moles". I guess V is the number of litres, T is the number of Kelvins etc

It is as if..... hell, something is measured in moles, but I haven't a clue what it is.

"n' is the amount of substance. The SI unit is the mole.

A similar case comes up in Ohm's Law

E = iR

the voltage equals the amperage multiplied by the ohmerage.

Oh No

the voltage equals the voltage multiplied by the resistance. That's better.

By killinchy (not verified) on 02 Mar 2009 #permalink

You paint chemistry with awlfully broad strokes. Have you ever met a physical chemist?

Grad:
He says it only with regard to the intro chem courses, not the teachers, which IME is pretty on the mark (there's a cursory explanation, but not a physics-level one).

On a related note, I've tried to get physics-level explanations out of my college organic chem teachers, and been met with a resounding lack of knowledge (I think I've yet to encounter one at my university that realized that orbitals were related to wave functions and resonance, which seemed obvious to me just *looking* at them in my intro chem courses)

Exactly right, I just mean intro chem courses. And that's not a fault, it's just that intro chem courses aren't stat mech courses by their nature since they actually have to teach how to do chemistry.

@ #1:
A significant fraction of high energy physics between 1950 and quarks consisted of doing just what you said. Observation drove the science, not theory. Ditto for nuclear physics and superconductivity.

@ #5:
You should see the chemistry book used in our intro class! Must have been written by a physical chemist. It has a nicer description of the Maxwell-Boltzman model (and the corrections to it) than most intro physics books. It puts stat mech out front. As one would expect, this works rather poorly with typical freshman chem students.

I like where you are going with this. First you get PV=nRT, then you notice the need for the van der Waals equation of state and try to predict the parameters from the bits you left out the first time (interactions between atoms and their size), seeing if you can get them from quantum properties of atoms. And so it goes for all branches of physics.

By CCPhysicist (not verified) on 02 Mar 2009 #permalink

CCPhysicist:
Which book was that, if you can recall? Actually, I'd love to find any (text?)book that approaches chemistry/organic chemistry from a physics/mathematical standpoint, rather than (in the case of organic) memorizing various mechanisms w/out adequate explanation of the physics behind them.

If you think chemistry is taught too much like tinker toys, you should check out economics. Almost all of econ, into the PhD level, is taught as a complicated semi-predictable combination of rules of thumb. Most of these rules amount to an extreme idealizing of the domain: "if we ignore these 42 things, and assume those things are zero, and pretend none of this ever goes outside a certain range, then this thing usually has a linear relationship with that thing." This approach has merit but makes the science only remotely connected with the reality.

This was arguably necessary until the advent of computers. Most aspects of economics lie in the vast range of complexity between classical gas law/fluid mechanics where the whole body is of interest, and billiard ball physics, insufficiently continuous for the former and too complicated for the latter, Now computers give us the ability to study economies as complex adaptive systems, with aspects of both gas/fluid and ball and much of their own (see the Santa Fe Institute) but it will be a long time before economics is taught differently - at least another generation or two.

hey...you wrote the ideal gas law like a chemist. gas constant? furry little burrowing animals? bah!

it should be:

PV=NkT

I always liked the Balmer series as an example of this kind of thing.

When Balmer discovered his series, he was basically doing numerology -- he simply discovered a mathematical pattern that fit the data of the hydrogen spectrum. However, it was Bohr who ultimately won the Nobel prize, for his proposal of a simple physical model that explained why the Balmer series describes the spectrum of hydrogen.

@ #7:
The author of that Chem book is "Tro". Take my comments with a grain of salt, since I've only looked at the thermo part of the text (that is where my physics class and their chem class overlap, without non-trivial differences in objectives as well as the approach to the problem). I have no idea if bonding is attacked from an atomic physics standpoint. I doubt it, since chemistry is taken as a freshman, before calculus-based physics.

The gen-ed physical science book I use (Hewitt et al) does atomic physics before chemistry, but not with any rigor. I know that a good friend took an honors organic course N decades ago that was based on atomic physics, orbitals, etc, but that might have been all prof and not the book. It was organic for chemists, not organic for pre-meds, so its entire purpose was different than the norm.

@ #10:
Another great example of what Matt was talking about, since the Bohr model was almost entirely wrong. The only thing it got right was the spectrum, but its many wrong predictions served to stimulate the experimental work and theoretical effort that led to real quantum mechanics - without orbits or "jumps".