Pique the Geek 26 October 2008: The Gas Laws and Absolute Zero

Crossposted at Dailykos.com

The mid to late 18th century was indeed a time of great intellectual awakening. Dr. Franklin made his myriad of discoveries, political discourse was taking an entirely new direction, and some upstarts in the American colonies were trying a grand experiment.

I want to talk about a series of discoveries made from the mid-1600′s through up until the very early 1800′s about how gases behave. This is evolution of thought brought about by the scientific method. We take a lot for granted now, but these discoveries took well over a century to perform and to understand.

The first of these discoveries is attributed to Robert Boyle (although he built of the work of others). It basically says that the volume of dry air is inversely proportional to pressure on the gas. Now, think about the tools that people had in the mid 1600′s. Crude, at best, by today’s standards. Very low capacity vacuum pumps, very crude compressors, and limited technology for measurement, mainly mercury filled tubes for measuring changes in pressure. To put the relation into a formula, it is simply

PV = k

where P is pressure, V is volume, and k is a constant for a given system.

Thus, if P is doubled, V must decrease by half to maintain the constant relationship. This leads to the relation

P1V1 = P2V2

where the 1 and the 2 refer to changing conditions, before and after a change, if you will.

With this variant, if you know the initial volume and pressure and either of the final ones, you can solve for the one that you do not know.

This sounds pretty elementary today, as all junior high physical science students are taught Boyle’s Law, but in 1662 it was pretty revolutionary. This relation was discovered completely experimentally; there simply was no theory either to suggest nor to explain it.

Jump to 1787: a French scientist named Jacques Alexandre César Charles discovered the relation between the volume of a gas and temperature. It states that the volume of a gas is directly proportional to the temperature. As a formula, it is written as

V/T = k

where V is the volume, T is the (absolute) temperature, and k is a constant for a given system.

Just as with Boyle’s Law, one can write

V1/T1 = V2/T2

so if you know any three terms, you can find the forth. Again, this is junior high subject matter now. His gas work was first published in 1802 by Joseph Louis Gay-Lussac, but Gay-Lussac attributed the initial work to Charles, so we call it Charles’ Law.

Gay-Lussac also published work of his own for an analogous relation between pressure and temperature,

P/T = k

where P is pressure, T is (absolute) temperature, and k is a constant for a given system, so we can also write that P1/T1 = P2/T2.

An interesting factoid about Charles is that he was the first person to fly in a hydrogen filled balloon. In those days, hydrogen was generated by passing steam through red hot iron shavings, sort of a dangerous method. “Terrified peasants” pretty much destroyed the balloon when it landed, so anti-science sentiment is nothing new, just better organized by Republicans these days.

This leads us to the combined gas law, one that integrates all of these relationships:

PV/T = k

where P is still pressure, V is still volume, T is still (absolute) temperature, and k is a constant for the system being studied.

By extension, the following relationship can be written: P1V1/T1 = P2V2/T2. In other words, if you know five of the six, the unknown one can be calculated.

OK, I am getting too wankish. But there is a concept that is essential for understanding the entire situation: for every degree Celsius a gas either expands or contracts by 1/273 of its initial volume (actually, 273.15, but 273 is close enough). That means, as any gas is cooled to -273.15 C, volume and pressure become zero. This is a physical catastrophe, because with no volume, matter ceases to exist.

This is absolute zero in temperature. The problem is that matter does not cease to exist. Well, that is probably not actually a problem, but it made those folks scratch their heads. Then the brilliant scientist Dalton made a very logical argument. It essentially goes: these relationships work well for temperatures and pressures that are not extreme. but at very high pressures or very low temperatures, the relationship breaks down.

Experience has shown this to be true. As our technology gets better, we have found that every gas can be solidified before the catastrophe occurs. That is, they are no longer gases. Why is that?

The fundamental reason is that the particles that compose any gas (either atoms or molecules) have a finite volume and behave as solids, in that they are incompressible. In other words, you can only pack them together so closely before those particles begin to fill up the space available to them. The gas laws are based on the assumption that gases are no more than geometric points, with no physical size or other properties. You just can not pack two atoms into the same space, but they did not know that back then, until Dalton speculated that matter was composed of some very small particles, rather than geometric abstractions.

This changed everything.

Once that was postulated, other thinkers began to examine the situation, and it was, over the course of only a few decades, that the atomic explanation of matter determined that the atomic model explained all of the observations and did not need any exception to “make it fit”.

The result was as a shotgun blast outside of your bedroom window. It awakened others, who capitalized on the concept and expanded it. Now we have modern atomic theory, and, whilst not complete, is completely in keeping with experimental observation.

Whilst it is fun and useful to be able to calculate volumes and pressures and such, the real contribution of the gas laws was the intellectual stimulation that explaining those laws produced. We would eventually have figured out that atomic theory is the correct one, but without the gas law work it likely would have taken longer.

Question, comments, and other scientific topics are, as always welcome.

Warmest regards,

Doc

Tags: Boyle, Charles, Dalton, Gas Laws, Gay-Lussac, Learning, Teaching