Monday, February 26, 2007

Digression on thermodynamics

We use terms like temperature and pressure as if they're obvious. On one level, they are. But on another level they're far from simple concepts. They are two pieces of a large branch of physics called thermodynamics. As the name implies, it's about heat - or least, that's how it started in the nineteenth century.

Back then, molecules and atoms were only an educated guess about the ultimate structure of matter. The microsopic nature of thermodynamics was unsuspected. Instead, the entire subject was developed with macroscopic concepts that approximated matter - whether solid, liquid, or gas - as a continuum, with continuous flows of work, heat, mass, and so on. Extensive thermodynamic quantities, like volume or energy, added as you grew a system in size; intensive quantities, like temperature and pressure, did not. Instead, these are defined as local averages of heat energy and force at idealized points in space. Around the middle of the nineteenth century, a rather mysterious quantity called entropy was identified and defined. It was somehow a measure of disorder and apparently never decreased, but it took another half-century or so for entropy's true nature to be unraveled.

Today, the definition of thermodynamics starts with order and disorder. Work is organized energy; heat is disorganized energy, distributed among a very large number of molecules whizzing and banging their way through space. They're so small, and they take up so little space in ordinary matter, that we can conceive of material as continuous without making much of an error. A body's impact force is all of its molecules moving in the same direction at once, and the body does work on whatever its pushing. Its heat is all of its molecules in a state of random agitation (random in the sense that their "heat motions" prefer no one direction). The level of agitation is measured by the temperature, which is an indicator of how much kinetic energy (energy of motion) each molecule carries. The pressure exerted by the body (which can be a gas or liquid - physicists and engineers call gases and liquids, collectively, "fluids") is the average force per area exerted by the random motion of the molecules pushing in all directions equally around the body's boundary.

Entropy is the best starting point for describing a system of molecules for which we have only partial information about the molecules' state. Thermodynamic equilibrium is that state of the system where all we know is its total energy, volume, and/or number of molecules. A system in equilibrium is characterized by a single temperature (essentially, the total energy divided by the number of molecules, or the average energy per molecule) and a single pressure (essentially, the total force exerted on the system boundary divided by the number of molecules and the area of the boundary). That part of the system's energy associated with the temperature is its heat content; that part associated with macroscopic motion pushing other bodies, its work. (The attentive reader will ask, what about the energy associated with the number of molecules - good question: that's the system's chemical energy, but we won't pause for that - it's only important if there are chemical reactions going on too.)

The world around us is not in thermodynamic equilibrium. In our climate, our oceans, the solid parts of the Earth - except in the far upper atmosphere, where the air is extremely thin - it's possible to define and measure pressure and temperature, but these will vary by position and time. The theory of climate (The Theory I called it a while ago) treats temperature and pressure as fields, which are functions that vary with where you are and what time it is.

Heat flows and air moves because temperature and pressure vary in space. Unequal temperatures in matter mean that there's more average heat energy in one place than another. Nature moves to correct that, by getting some of the heat energy to flow from higher temperature to lower. Similarly, unequal pressures means unbalanced forces in the medium. The region with higher pressure will press against the region with lower and partly displace it. Both phenomena are examples of the second law of thermodynamics: a system not in thermodynamic equilibrium will evolve in such a way as to increase the total entropy and move itself towards thermodynamic equilibrium. The nineteenth century's macroscopic thermodynamics, this law had no obvious explanation. With the twentieth century's microscopic or statistical thermodynamics and entropy defined in a fundamental way as molecular disorder, the Second Law is just an expression of probability: the more disordered state is the more probable. The heat and air flows move the climate from a less probable state to a more probable one.

This is also the exact sense in which thermodynamic differences help to drive climate. As the climate changes, entropy increases. On the other hand, certain other physical quantitites are conserved or fixed in time - the energy, the volume, and the number of molecules. In real climate, these aren't exactly fixed, but they almost are.

Labels: ,


Post a Comment

<< Home