Temperature

Eli wants to eventually discuss the details of what happens when a greenhouse gas molecule in the atmosphere absorbs an IR photon and later the process leading to emission of IR photons from greenhouse gas molecules in the same volume of atmosphere.  To do so requires some background.

There are times when you just feel good about yourself. These especially include times when you are trying to explain something and you find that your understanding is as good, if not better than what you find in the literature.

Temperature, everybunny knows what it is, but it turns out that it really is a lot more.  One of the most interesting things about temperature is that the concept is relatively new.  Hotter and colder, warmer and cooler, yeah those are old timers,and accessible to the senses at least if the differences are extreme.  For example, who can accurately tell the difference by touch between the temperature of a piece of wood and a piece of iron if they are close, but the ability to measure temperature instrumentally,  is only a few hundred years old.  The Chinese, who basically invented everything never got around to temperature and had no thermometers.

While there were earlier devices that could be used to compare temperatures, the first devices that were used to measure temperature appeared a little before the middle of the 17th century in Europe.  The development of thermometers is tightly tied to the development of thermodynamics and heat engines.  Thus, it is really a wonder that even a few instrumental records exist before 1700. 

A useful way of starting is to define temperature as a property such that when two bodies at different temperatures are placed in contact the net heat flow will be from the one at higher temperature (the warmer) to the one at lower (the colder) temperature.  The outcome has to be that the temperature of the colder body will increase and that of the warmer will decrease.  Technically it has to be stated that no work should be involved in the process.  It's easy to see then that the two bodies will eventually reach the same temperature and at that point they can no longer exchange net heat so they will stay at that temperature.  They will be in equilibrium.

The ability to measure temperature depends on the zeroth law of thermodynamics, that if you have three bodies A, B and C (to be contrary M, N, and P if you want), if A and B are allowed to exchange energy in the form of heat, at equilibrium no net heat will be exchanged between them.  Similarly if A and C are at equilibrium.  The zeroth law states that B and C must then also be at equilibrium.

Now let one of them, say A be a thermometer, something that indicates temperature whatever that is.  That means that A and B and C will be at the same temperature. But what is the temperature?

Also how to measure it.  The first answer was the air thermometer.  A glass bulb with a volume of air sitting on top of another bulb filled with a liquid and connected by a tube.  As temperature increased the pressure in the air bulb increased, depressing the liquid level in the tube.  Galileo was one of the first to come up with this, but it took Robert Hooke in 1665 to figure out how to make a useful temperature scale.  Hooke's thermometer became the primary standard in England against which other thermometers could be calibrated and was maintained by the Royal Society.However, you had to bring your thermometer to Hooke's at Gresham College to calibrate it as the scale was whatever Hooke had scratched on his thermometer.  Also, air thermometers are subject to atmospheric pressure changes.  In Hooke's case, his thermometer is A, yours is B and C is what you are trying to measure the temperature of.  Hooke's readings form part of Manley's Central England Temperature series, but Manley does not appear to pay much attention to the precision of the instruments, being more concerned (and rightly so) with things such as time of observation and altitude corrections

Fahrenheit came up with the mercury in glass thermometer and also the idea of using fixed points such as the melting point of ice (the upper point defining the scale was 96 F, body temperature) to define a scale, dividing the interval by a convenient number of steps.

The next step is the ideal gas law, that for an ideal gas, T = PV/nR where P is the pressure of a gas, V the volume, n the number of moles (or molecule) and R a constant.  For an ideal gas there are no interactions between the molecules and the molecules have zero volume.  There is no ideal gas, but in the limit of low molecular density n/V --> 0 all gases approach ideal and we can use the extrapolated values of PV/n to define an absolute zero for temperature where the product PV of the gas goes to zero.

One other temperature is needed to define a scale.  That choice is arbitrary, but it has been chosen to both make the intervals of the scale (the degrees) agree with the previously established Celcius scale and to allow calibration free of a primary thermometer.   This is accomplished by defining the triple point of water as being 273.16 K above the absolute zero.   A triple point is a combination of temperature and pressure such that all three phases, liquid, solid and gas exist simultaneously.  At the triple point if the temperature or pressure change by the smallest amount one, or two of the other phases disappear.

The ideal gas law (and the second law of thermodynamics) can be used to define absolute zero.  What temperature is on the molecular level requires Gibbs, Boltzmann and statistical mechanics.

(For details see Temperature, by T.J. Quinn  or ZTemp)