Thermodynamics
This is a big field and you could spend your life on it. We will cut to the chase and just point out some important fundamentals. One application is on engines that make use of heat (such as an automobile engine) and we will concentrate on the energetics of the engine without worrying about the details of how it works. By the way, when we say "heat" we mean heat energy (thermal energy).
The laws of thermo (sort of):
1. You can't win.
2. You can't break even.
3. You must play the game.
We consider three quantities of energy only, and let's make them positive by definition: QH, the heat energy input at a high temperature TH; QL , the heat energy output at a lower temperature TL; and W, the work output of the engine. Assume that these are the only energy transfers and that our engine is warmed up, so applying the conservation of energy principle (the first law of thermodynamics), we find that
QH = QL + W (equation 1).
We are dealing with an idealized engine here. An actual car engine has gasoline input which explodes in the cylinders, giving off energy equivalent to our QH. The QL in real life consists of several outputs of heat at different temperatures (heat out the exhaust, air circulating around the engine, water/antifreeze circulating through the block and then air-cooled in the radiator), but to simplify things, say its waste heat is delivered at one temperature, TL.
W is a complicated term also. When the gasoline explodes and the high pressure pushes on the piston and does work, that is just part of the story. At all other times, negative work is done, i.e. the thing is a drag. When we say W we mean the net work output of the engine.
A typical car engine might have a W of 1 kilojoule (kJ) for each cylinder during the time of two rotations of the crankshaft (one firing of each cylinder). To do this requires about QH = 4 kJ worth of gasoline burned in each, and then the other 3 kJ is the QL or waste heat.
Now for a little digression about entropy. When you heat something up, the thing gains entropy; cool it off and it loses entropy. In heat we define entropy change of a body as heat added to the body divided by its absolute temperature, and make it positive if heat is added and negative if heat is taken away. (Other kinds of entropy will be discussed later.) Now consider a warm object snuggled up against a cool one, and keep your fantasies in check. Some heat (Q) will leave the warm one and enter the cool one, and in terms of entropy change, warm loses Q/Twarm and cool gains Q/Tcool. Look at the denominators, and you see that the gain of entropy is greater than the loss, so the sum of the changes of entropy is positive.
Because heat always flows from higher to lower temperature, the gains of entropy will always be greater than the losses. The proof above is for a simple case, but it turns out that the principle is true in general: We denote entropy change as D S, then if we keep track of all entropy changes in an isolated system,
S D S >
0 (equation 2)
This is known as the second law of
thermodynamics, and it is really a big deal. Besides the heat transfer dealt
with here, there is entropy change due to changing the arrangement of
molecules. Changing from crystal structure to a more random arrangement is an
entropy increase. Entropy is a measure of disorder, or randomness. We could
talk about high entropy areas such as your instructor's hair or desk (speaking
metaphorically), but let's get back to the engine and stick to DS = DQ/T.
Recall that to run the engine we extract
energy QH from something hot (so the hot body loses entropy) and
deliver waste energy QL to something with lower T (which gains
entropy). To maximize the efficiency, we want as little waste as possible, but
nature, through the second law, does not permit QL to be very low. A
modern power plant is typically about 40% efficient, which means that W is 0.4QH
and QL is 0.6QH. The best theoretical efficiency (which,
like the perfect vacuum, is not achievable) is the case where S D S = 0, so
entropy loss = entropy gain, or
QH/TH = QL/TL
(equation 3, for the ideal case).
Efficiency is roughly defined as what you
want to get out of it divided by what you need to pay for. In the case of the engine,
it is
e = W/QH (equation 4).
Solving equation 1 for W and substituting
above, we find e = 1 - QL/QH. This is for any engine. Now
for the ideal maximum efficiency, rearrange equation 3 to get QL/QH
= TL/TH. Hence
emaximum = 1 - TL/TH or e < 1
- TL/TH (equation 5)
Here is how you can get somebody's goat:
Make the claim that you know how to use heat to produce work at a higher
efficiency than this. (There are kooks all over who think they can get energy
from pyramids or crystals or that a slab of marble is always cooler than its
environment….People hearing your claim will think that you are a kook). Well,
here's the deal: If you just do half a cycle and then quit, you can exceed the
e limit of equation 5. For example, have heat drive a piston one way (and if
you want to reduce friction, make it a liquid "piston"). Equation 5
is for a cyclic engine, and it does not apply if you don't complete the cycle.
Here is a simple example: The environment is
300 k and you have a source of heat at 400k and there is nothing
warmer nor colder than these extremes. Everybody knows the emax= 1-300/400 = 1-3/4 = 0.25. A simple case of
an expanding gas is the constant pressure case. W = PD V = nRD T, and heat added is nCp
D
T, where Cp is the molar heat capacity at constant pressure. For an
ideal monatomic gas, Cp is 5/2 R, so W/QH is nRD T/(5/2nRD T) = 0.4.
We win! The efficiency for that incomplete cycle is greater than the emax. It is completing the cycle where you must
do negative work and dump off that waste heat that is the killer of efficiency.
The pressure-volume graphs below sum it up.
The area under the curve is the work done. On the left we have the area under
the horizontal segment for the expansion only, but the cyclical case on the
right requires negative work to bring the piston back, so you are left with
only the work enclosed by the rectangle.
Electricity does not have the 2nd law efficiency limitation, but you need to consider the source of the electricity. You can produce electric heat with 100% efficiency, but if it came from a power plant with 40% efficiency, which is typical, you are worse off in terms of fuel burned than if you had burned the fuel yourself. Furnaces have much better than 40% efficiency.
A related issue: When fossil fuels are too expensive to use for energy sources, one of the tough questions people will need to consider is how big a home power plant is needed? Those solar panels may become fairly cheap, but you would probably need to invest thousands of dollars extra to be able to brew coffee or use an electric hair dryer. People living in abject wealth would want to do this, of course, but the rest of us would be smart to make some adjustments in our lifestyles.
Another related issue, speaking of fossil fuel becoming too expensive, is the electric car. Petroleum prices will go ballistic before coal prices, so people will charge their batteries by means of the coal-burning power plants. The overall efficiency is greater than the gasoline engine, and it turns out that the coal-electric car system puts out a lot less global-warming CO2. Better yet, charge them with wind and solar electricity. The hybrid car, electric motor + gasoline engine, is a temporary partial remedy.
Another good system would be to use wind, solar, or ocean wave energy to
break down water into hydrogen and oxygen (sea water could be used). Then use hydrogen
in internal co
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Comments, questions: email fredrick.gram @tri-c.edu (remove space before @)