Friday, April 20, 2007

Radiation, conduction, convection, evaporation: A précis

Sometimes all these mechanisms for transferring heat get a little complicated and hard to remember. So time for a time out, to explain each in turn, how they're similar and how they differ. Some homey examples and analogies should help too.

First, what heat is: it's disorganized energy, disorganized at the molecular or microscopic level. It represents entropy, a quantitative measure of disorder. In thermodynamics, heat is usually contrasted with work, which is energy organized at the "large" or macroscopic level. Both are measured in a common energy unit, the joule. In the old days, heat was measured separately in calories, but for various good reasons, all forms of energy are quoted today (at least by physicists and more and more by chemists) in a common unit. A calorie is about 4.2 joules.

Temperature is a measure of how disorganized the energy of a system is. When a system is at thermal equilibrium - that is, its energy is as disorganized as it can be - temperature is a measure of the "typical" energy distributed to each tiny microscopic degree of freedom, each independent motion the system's microscopic components can execute. In equilibrium, by its nature, the average energy of each degree of freedom is the same. If the system is not in such a state, it's not in thermal equilibrium. In such cases, it's often possible to assign a different temperature to each subsystem, suitably defined, and the system is said to respect local thermal equilibrium (LTE for short - that is, not global - such a system has no single temperature). The Second Law of thermodynamics tells us that varying temperatures imply heat flows from higher to lower temperatures. In the real world, it's best to think of heat flows as fundamental and the variable temperature distribution as an effect, not a cause.

The Second Law also implies that such heat flows act to move the system in the direction of greater entropy and thus "towards equilibrium." All the Second Law requires is that a system not in equilibrium move "toward equilibrium." It doesn't specify the mechanism of entropy increase, or how fast the movement is, or that the system ever reach equilibrium. Those are the details that depend on the exact nature of a system's constituents and forces.

The three standard mechanisms of heat transport - conduction, convection, and radiation - all move heat from higher to lower temperature and generate increasing entropy along the way.* So does evaporation-condensation - it's often lumped together with either conduction or convection, but it's helpful to separate it out as a fourth, distinct mechanism in its own right. Depending on the exact details, one mechanism is more or less efficient than the others; the most efficient mechanisms dominate the heat flow. (The most efficient are the ones that generate the least entropy for moving a given amount of heat.)

The different mechanisms can be divided or contrasted in at least three ways, and these distinctions help to define the them.

1. The most fundamental distinction is the medium of transfer. Heat can be the disorganized motions of matter particles (molecules). The molecules themselves don't have to move far or, on average, move at all, to transfer heat to their neighbors by collisions. Or they can execute organized, coordinated motion. Conduction, convection, and evaporation-condensation all fall into this category.

The other disorganized particles that can carry heat are photons, the particles of radiation.

2. Some heat transfer moves heat in more or less straight lines, which is pretty efficient. Convection always works this way. Evaporation-condensation, if combined with convection, also moves in straight lines. Liquid water absorbs enough heat to convert to vapor, moves as an organized mass somewhere else, then condenses and dumps that heat at that somewhere else. Radiation can as well, if it moves through a material medium transparent enough to not pose much of a barrier.

The opposite of straight-line transfer is diffusion. Molecules bang into one another, or photons get batted from one molecule to another, in an almost random way. I say almost random, because it isn't quite! The system isn't in thermal equilibrium (remember: heat is flowing), so there's a slight bias. On average, the more energetic molecules transfer heat in the direction of lower temperature (or the more energetic photons move that way). But there's a lot of jostling around along the way. As you might imagine, it's generally a less efficient way to move heat. In matter, heat transfer by diffusion is called conduction. It's common, depending on the density of material. And radiation can also diffuse, if it's moving through a material medium absorptive (opaque) enough that it can't move in a straight line. Instead, photons are absorbed and re-emitted multiple times before their heat gets across the medium. The plasma of a star's interior is the classic home of radiative diffusion, as was the early Big Bang. For infrared radiation, the wet air that appears transparent to us poses a partly opaque barrier that can only be traversed by diffusion.

3. The third great division is between heat transfer mechanisms that require phase changes in matter and those that don't. A phase change is like the change of liquid to vapor, or ice to liquid. It's a qualitative change in how the molecules are organized, from one state of matter to another.

Evaporation-condensation is obviously such a mechanism; it needs two phase changes to work, one to absorb the heat somewhere, the other to dump it back somewhere else. Evaporated water molecules can get from somewhere to somewhere else by diffusion or by convection. In real life, it's by some mix of the two.

A more difficult fact to appreciate is that convection itself also requires a phase change. Without convection, there's no large-scale, organized flow of heat. Under the right conditions, convection "switches on," and matter parcels, eddies, or "blobs" that are overheated relative to their surroundings move the excess heat from their origins to their destinations, where they give up the excess heat and lose their identities as distinct "blobs." The phase change here is from a state of "no macroscopic motion" to a state of "macroscopic motion."

Why does convection happen at all? And where does it happen? Convection might seem counterintuitive in light of the Second Law. After all, if a system is supposed to get more disorganized over time, how can it switch to a coordinated, macroscopic movement of overheated blobs? The answer is that such movements don't violate the Second Law; they fulfill both its letter and spirit in a subtle way.

Convection requires work to move the overheated parcels from one place to another, if that motion has to overcome friction, gravity, or other forces that otherwise would hold them in place. That work has to come from stored heat, in apparent violation of the Second Law. But - if the blob is overheated enough compared to the temperature of where it's going, by dumping its heat in the cooler location, it can increase the total entropy, which is all that matters for the Second Law. The decrease in entropy needed to convert disorganized heat into organized work is more than compensated by the increase in entropy once the heat gets to the cooler place where it's going. By Second Law accounting, convection "pays" in such cases, so to speak. There's an exact formulation of this condition, called the Schwarzschild criterion, that decides when and where convection switches on.**

We're familiar with this in everyday life. If you heat a pan of water on the stove, you can get heat currents going only if the temperature contrast between the bottom layer of water and the layers above is big enough. Then it starts to boil, and you actually see the blobs of overheated water rising (often with air bubbles carried along), doing work against gravity, but also transferring heat upwards to the cooler layers. The same thing happens in the atmosphere and especially in clouds. The distance over which the blobs retain their distinct identity as overheated relative to their surroundings is called the convective mixing length.

Except for very smooth convective flows, convection in fluids is turbulent, a concept that has an exact meaning we'll learn about later. That makes it very hard to understand in detail. Turbulence is actually a larger phemenon in the atmosphere that encompasses a wide spectrum of spatial sizes and velocity scales. Convective heat flow is just one slice of turbulence, with overheated blobs of a certain size moving within a certain range of speeds. The full theory of convective fluid flow is impossible to solve, so physicists and engineers use approximations, some better than others, but none really accurate in all situations. And while evaporation-condensation by itself is fairly simple, the combination of evaporation-convection-condensation is really hard, even more difficult than convection alone.

Heat transfer in the atmosphere. The air is too thin for conduction, or matter heat diffusion, to be important. Radiation is the main way heat is transported in the lower atmosphere and the exclusive mechanism in the upper atmosphere. For the infrared type of radiation the Earth emits from its surface, the atmosphere is fairly opaque and the heat transfer mildly diffusive.

But in the lower atmosphere, convection and evaporation-condensation also play important secondary roles. In clouds, which are so opaque that radiative transfer is suppressed, condensation and convection are the whole show. Anyone who's flown in a small plane through thick clouds has experienced this fact first hand.

Heat transfer in the oceans and underground. Conduction is important here and actually the main mechanism. Convection does play an important role in the oceans, however, and even in the solid Earth, where plumes of heat from the core rise to the surface and appear as geysers, volcanoes, etc.
* How much entropy? The increment (differential) of entropy is dS = dQ/T, where dQ is the increment of heat. (That relation defines temperature.) The net entropy created by moving the same amount of heat dQ from higher temperature T1 to lower T2 is dS = dQ1/T1 + dQ2/T2, where -dQ1 = dQ2 = dQ > 0 is the amount of heat released at T1 and absorbed at T2. The Second Law requires T2 <>1, so dS = dQ*(1/T2 - 1/T1) > 0. That is, the total entropy increases on net. This is the Second Law in quantitative form.

** If you've read about black holes, you've surely heard of Schwarzschild, a slightly older contemporary of Einstein. Same brilliant Schwarzschild, different branch of physics.

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At 12:09 AM, Anonymous Anonymous said...

:D i have an assignment on conduction, convection, radiation, and evaporation, and this was really helpful, thanks a lot ! :D

At 11:24 PM, Blogger Binah said...

You're welcome. I hope I got everything right and clear.


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