Concepts in Thermodynamics¶
Macro vs. Micro¶
Statistical Mechanics deals with counting particles and deriving the macroscopic properties from microscopic assumptions.
Thermodynamics, on the other hand, is almost purely devoted to understanding the macroscopic quantities and how they behave in the real world.
Pressure¶
The first discovered and likely most important concept is Pressure.
Pressure is a force per unit area, a scalar field. It has no direction. That is, if a point has so much force it exerts in the downward direction, then it is applying the same force in all directions.
Units of Pressure¶
Pressure is often expressed in units of Pascal (Pa). 1 Pascal = 1 Newton / meter^2.
Pascals are awfully small units. The air pressure you are used to has roughly 10^5 Pascals – that’s the force of 100,000 kg on a square meter, or 10 kg on 1 square centimeter. That’s an enormous force. You might see people use kilo-Pascals (kPa) for various things, but typically when we move into atmospheres, we either keep the 10^5 or we just use units of atmosphere.
We also use bars (bar) where 1 bar = 10^5 Pa. A millibar is 1/1000 of a bar and thus 100 Pa. Typically, we use the bar to measure the difference from standard pressure, for things like weather.
Chemists typically use atmospheres (atm), where 1 atm is the standard pressure at sea level. 1 atm is 1.013 x 10^5 Pa. Since most of their chemistry is assumed to work at or near sea level pressures, this is a convenient unit for them. Physicists, on the other hand, are interested in extremes and limits.
Measuring Pressure¶
In order to accurately measure pressure, you can use a device that either measures force against a known area, or a tube filled with mercury. Mercury is a liquid with constant density, and when held vertically will create a (near perfect) vacuum between the top of the glass and the top of the mercury. We can assume that that pressure is 0 or near zero, and then compare how high the mercury is on the other end of the tube in a sort of U-shape.
We are also very interested in the Gauge Pressure, the pressure difference between the thing we are observing and the ambient pressure (the pressure of the atmosphere at that elevation, time of day, weather conditions, etc…) The Gauge Pressure tells us things like whether things will blow up or whether you can open a seal.
Using Pressure¶
Pressure is known to affect temperature and volume of substances.
Increasing the pressure tends to decrease the volume, and vice-versa.
Increasing the pressure tends to increase the temperature, and vice-versa.
Note that solids and liquids tend not to change their volumes, so they tend to maintain constant volume (more or less) under different pressures.
Calculating Pressure¶
Calculating pressure at any given point is rather easy.
All you need to know is how much force is being applied across any particular area.
In the case of the atmosphere, you can add up all the mass of the air above the point in question, multiply that by little g, and you get how much force is being exerted. The weather may also play a role in the pressure at a given point, but the net effect is that the atmosphere is just slightly thinner or thicker, or the density of the atmosphere has changed.
If the system is not exposed to the atmosphere, then you need to allow a free-moving area and figure out how much force is being applied to that.
Composition of Pressure¶
When two systems of gas are brought into mechanical contact, such that they can exchange pressure, the pressure will equalize, with the higher pressure flowing into the lower pressure until an equilibrium is reached.
History of Pressure¶
Pressure was poorly understood, even since Aristotlean times. The assumption that Aristotle made, that the atmosphere had 0 pressure, was clearly wrong, but it would take until Pascal to totally disprove it. He based his work off of some observations by Torricelli, who should likely receive credit for the idea that the atmosphere did not have 0 pressure.
The story goes that the Grand Duchy of Tuscany was trying to pump water with a siphon mechanism. They noticed that beyond a certain height, the siphon would stop working. They asked Galileo to look into it, and Galileo passed it off to Torricelli. Torricelli in his investigation of this phenomena came to realize that a vacuum was being created in the siphon, and that the vacuum was not able to suck the water up the pipe beyond a certain height. Galileo had taught that “nature abhors a vacuum” which is a way of saying that pressure “sucks” things into it.
Torricelli came up with the novel idea that it wasn’t the vacuum sucking – it was the atmosphere pushing the liquids, and there was only so much pressure. He was able to do several experiments to show the properties of pressure, including one where he inverted a full tube mercury creating a space, as well as poking holes in a tube and showing how water would flow out of the holes at different rates depending on how high the holes were.
Blaise Pascal was able to get Torricelli’s ideas accepted into the general scientific population. He challenged the scientists of his day to a duel of predictions. What would happen if we inverted a tube of wine? It was well understood that wine would emit vapors that would cause the liquid to condense on the side of a wine glass (unlike pure water) and so it was assumed that the space above the wine was filled by evaporated wine.
After the predictions were made, Pascal inverted a tube of wine, similar to Torricelli’s experiments with mercury. Surprisingly, the wine maintained a steady height above the level of the basin, no matter how the tube was moved, proving that the space above the wine was actually empty – a true vacuum. More vacuum does not suck harder than some vacuum, so indeed, it must be assumed that the vaccum creates no sucking forces whatsoever.
Pascal’s cousin then performed an experiment where he carefully measured the level at different elevations, showing that as you increase in elevation, pressure falls, and making it possible to predict the height of the atmosphere, beyond which is pure space.
With this, experiments began to investigate the behavior of pressure in weather patterns, and the connection between high pressure = clear weather and low pressure = stormy weather was made.
Number of Particles¶
Up until the 20th Century, physicists did not accept that the universe was composed of atoms. They felt it was speculation at worst, a convenient trick that chemists used at best. There were a few physicists who insisted on the atomic nature of matter and even developed a system whereby predictions about thermodynamics could be made simply starting with the assumption that matter was atomic.
That said, for much of thermodynamics, the exact count of particles isn’t terribly important. Like chemists, we are worried about the relative number of particles in each system rather than an exact count on the total number of particles.
Chemists have measured the number of particles in units of a mole. The