LAWS OF THERMODYNAMICS TOD CANADA THE OIL DRUM

TOD CANADA

THE OIL DRUM
THE OIL DRUM CANADA
LOIS DE LA THERMODYNAMIQUE

In this house we obey the laws of thermodynamics!
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Posted by Libelle on December 30, 2008 - 11:11 pm in The Oil Drum: Canada
Topic: Miscellaneous
Tags: energy, entropy, heat, original, thermodynamics, work [list all tags]

When you use energy, the rules are well defined. The first and second laws of thermodynamics have been well understood for more than a century, and the third a little more than a century, but the topic is still considered by most to be rather obscure. That is unfortunate, because these two laws are so important, and because almost everyone has a good understanding of the first and second laws, even if they think they do not. Understanding the implications of the legislation is another matter.



There are many versions of mischievous acts. All I like most is:


(zeroth law) You must play the game
(first law) You can not win.
(second law) You can not break even on a very cold day.
(Third Law) It is not cold.


They are surprisingly accurate.

The laws are, it should be recalled, experimentation at the outset. The world has been found to work that way.




Zeroth law
The zeroth law actually states that if two systems A and B are in equilibrium with each other, and systems B and C are also in equlibrium with each other, then systems A and C are also in equilibrium with another. Another way, is that situations like Escher "Waterfall" will not occur in real life.

You must play the game




First law
The first law is the law of conservation of energy. It includes the equivalence of heat and working conditions, but is more general in that there are many forms of energy are interconvertible, but the total for an isolated system remains constant over time. One point that is often misunderstood is the role of the equation E = mc2. It is usually refer to a conversion of matter into energy, but the reality is more simple. Energy is the mass, the equation and tells you how. Whatever the conversion takes place in an isolated system, its total energy (and hence mass) remains constant.

You can not win.




Second Act
The second law is that which results from the observation that hot losing heat to cold things. This is a one-way process. Mechanical work is transformed into heat. The heat can be converted into mechanical work, but there are limits. The implications of this are far and an amount can be deducted (and defined) from this experience and thought.

If we have two heat reservoirs (both practical infinite capacity) at different temperatures, then we can build devices that take heat from the hotter reservoir, turn some of them into mechanical work and reject the rest to the cold tank. The rejection of some of the heat was considered inevitable, but the amount of waste heat becomes less than the temperature of the heat source is high. In the absence at this stage to define what we mean by the numerical value of the temperature, we assume that the maximum conversion efficiency is a function of both temperatures. Engine efficiency is generally defined as [working in the heat], but in this case, I will look at [the heat of the heat] or [1 - effectiveness]. If temperatures are two tanks T1 and T2 and heat from the T1 is warmer and the heat released in q2 is cold, then we say that:

q2/q1 = F (T2, T1) F is an unknown function (an algebraic expression) of the two temperatures.

Maximum efficiency implies the reversibility of the process. An example of this is that the heat transfer hottest tank engine must take place without any difference in temperature between the tank and the engine that absorbs heat. If there is no difference, the heat engine operates at a lower efficiency (smaller temperature difference between hot and cold), and it would not be possible to run the process backwards (no heat flow "upstream"). There can be friction either. The engine with maximum efficiency is reversible and can be used as a heat pump, pumping heat from the reservoir of the fountain hottest and requiring mechanical work to do. The values of Q1 and Q2 are the same as in the case of the engine, but the direction of flow is reversed and the work is put into the system rather than be taken. The absence of differences in temperature between the engine / heat pump and its heat reservoirs also means that the process will be much slower, but it is the case for all these machines ideal.

Now suppose we have a third heat reservoir at a lower temperature still, T3, and a second engine that operates between the second and third reservoirs. If the heat from the second tank is q2 (rejected by the first engine) and has rejected the third q3, then:

q3/q2 = F (T3, T2)

But we could instead have used a motor directly between the first and third reservoirs. This engine must have the same efficiency as the combination of the other two, because if it did not, then the heat could be run continuously around the cycle of three engines, using the power of one or two engines driving the other (s) to the rear, leaving a net work with the production of heat is taken from a single reservoir. This is not consistent with the way things work. So:

q3/q1 = F (T3, T1)

But: q3/q1 = (q3/q2) x (q2/q1)

So: F (T3, T1) = F (T3, T2) x F (T2/T1)

If you have not turned off at the beginning of algebra, it should be obvious that this is a very serious restriction on the nature of the function F. During the last equation, T2 on the right side disappears, as a result of simple multiplication. This means that F (T1, T2) must be of the form f (T1) / f (T2), where f is another function.

So: q2/q1 = f (T2) / f (T1)

May you not forget that I started this argument without defining what is meant by a temperature. This equation gives us the opportunity to define a temperature scale, by selecting the function f. That's what William Thomson (later Lord Kelvin) was in 1848. He chose f (T) to be as simple as possible:

f (T) = T

So: F (T2, T1) = T2/T1 and T2/T1 = q2/q1

In other words, an absolute temperature scale can be defined as a function of engine thermal properties are independent of any substance. If an ideal heat engine has a conversion efficiency of 50% (half of the heat is converted into work and half of the heat rejected), the ratio of heat to the temperature of heat source temperature is 2 - by definition.


To complete the definition of such an absolute temperature scale, we need to define the size of a diploma. If we measure size as the difference between the freezing and boiling water is 100 degrees, we have a scale that may correspond to the Celsius scale, but with a lag corresponding to the point of freezing of water on the absolute scale. This discrepancy is 273.15 degrees and now we have the Kelvin scale.

Entropy
The idea of entropy is associated in most minds with the ideas of order and disorder (entropy higher = more disorder). That is correct, but the origin of the idea comes from the flow of heat. If a quantity of heat q enters a system (absolute) temperature T, then the system increases the entropy of q / T. That is the definition of entropy. If we look at the first heat engine above, the entropy of the hot reservoir decreases q1/T1 and the increase of the cooler by q2/T2. If the engine is reversible, q2/q1 = T2/T1, so the overall change in entropy is zero. It is a characteristic of the process is reversible. In real process, the total change of entropy is always positive. One example is the flow of heat from a warm body to a cooler - the hot body loses entropy, the cooler, but we win more than one has lost the hottest since the T in the q / T is the most small and q is the same.


Available work, or Exergy
The maximum amount of work that could be extracted as a product of a process (ie, if it produces a reversible manner) can be easily calculated from energy and entropy changes between States of departure and arrival process. This is sometimes called the exergy available initially. Just how it is derived in May May be another assignment. Exergy, unlike energy, may be destroyed. The ideal of work is never done, of course, but it is fairly simple to show that the exergy irretrievably lost when an irreversible change takes place is equal to the increase in entropy associated with the irreversible, multiplied by the temperature of the environment in which the process takes place. This is the lowest temperature at which heat can be rejected by the process. It follows that if the ambient temperature is absolute zero, there is no loss of exergy or available work, no matter what.

You can not escape, even on a very cold day.




Third Law
There are two ways of the third law by stating:

The entropy of each pure substance at absolute zero is zero.
It is impossible to achieve absolute zero in a finite number of steps.

The reason why the second follows from the first is that any process that reduces the temperature of a substance must contain a step in which the change of entropy. If any of the entropy is zero, then no change of entropy are possible and there is no way to do it for cooling. In fact, the law is observed that the change of entropy is always zero. It is easy to declare all entropies zero at absolute zero, which corresponds to the statistical interpretation of entropy. It can get very close (in degrees) of absolute zero - the current record is around 10-10K, but it gets closer, it becomes more difficult to cool.

It is not cold.




160 In the comments on this house, we obey the laws of thermodynamics!
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   Gail the Actuary on December 30, 2008 -