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Thermodynamics

For any discussion on energy the most useful part of Physics is that concerned with Thermodynamics. In "lightandmatter" one is refered to book 2 page 146 for the basic information.

Before the kinetic theory of gases was fully developed, there was an inkling that mechanics and heat were related in some way. James Watt (1736 - 1819) in 1776 had built a steam engine and Nicolas Léonard Sadi Carnot (1796 - 1832) had written his treatise La Puissance Motrice du Feu ( a propulsive force from heat) in 1824 which related the amount of work available from a heat source.

Now, thermodynamics can be an intimidating subject as it is usually written in a formal language and a "glimpse" does not do it justice. However, it is hoped the there will be an eagerness to continue elswhere once the importance of the subject is appreciated.

A simple fact - one can warm one's hands by

(a) rubbing them together ie doing work, say, deltaW, a small amount of work

(b) by heating them infront of a fire, ie injecting heat energy, say, deltaQ, a small amount of heat transfer

so the increase in internal energy of our hands has come from both sources i.e. deltaU = deltaQ + deltaW

Carnot's theory is based on subjecting an ideal gas to the following cycle - a-b, b-c, c-d and d-a. All temperatures need to be measured in °K ( °K = 273 + °C). ( see "lightandmatter" page 146) Work on the gas and heat applied to the gas will be considered positive whereas work done by the gas and heat given out by the gas will be negative.

A very artifical "engine" was envisaged for this cycle, just a cylindar and a piston. This assembly was moved bodily from a cold plate to an insulating plate and then to a hot plate and finally to the insulating plate. One must remember that we are still in the realms of a theoretical world .

So the "engine" has the following description

One can understand the energy involment by looking at the following diagram:

In any cyclic process the internal energy of the gas must return to the starting point and hence the red line, after d -a stage, returns to the original level. More work is given out by the gas, stage c-d, than the work done on the gas in stage a-b so we do have an engine capable of doing work. To provide this work there must be an input of heat energy and one can see that the heat in for stage c-d is much more than the heat out in stage a-b. After a little algebra, the efficiency of converting heat to work can be found to be:

                                                             efficiency = 1 -  T(cold)/T(hot)

The analysis of thermodynamic cycles is well covered on many web sites. The Wikipedia site uses Entropy - Temperature graphs instead of the pressure - volume presentation used here.

Well, why is it so important? It is fair to say the the whole automobile industry, in particular, and transport system, in general, is based on thermodynamics. Electrical generation needs a heat to mechanical link and, here, inefficiencies lead to hugh energy losses. Say a power station has T(hot) at 600 °K and T(cold) at 400 °K then the efficiency of conversion of heat to work is 33 %. Therefore 2/3 of the heat will be wasted simply because the Carnot cycle cannot be made more efficient. Most Scandanavean countries have used the 2/3 low grade heat to provide towns with district heating but, in the UK, this heat is mainly dispersed into the environment.

It must be realised that many other scientists contributed to studies on Heat, most noteably Robert Boyle (1627 - 1691), Joseph Black (1728 - 1799), Benjamin Thompson, Count Rumford (1753 - 1814), James Prescott Joule (1818 - 1889), Rudolph Clausius (1822 - 1888), William Thompson, Lord Kelvin (1824 - 1907) and Walther Hermann Nernst (1864 - 1941).

Wikipedia list several thermodynamic cycles and the animations for the alpha and beta variants of the Stirling cycles is particularly helpful. The list is given below :-

:[[Atkinson cycle]]

:[[Brayton/Joule cycle]]

:[[Carnot heat engine|Carnot cycle]]

:[[Diesel cycle]]

:[[Ericsson cycle]]

:[[Hirn cycle]]

:[[Kalina cycle]]

:[[Miller cycle]]

:[[Four-stroke cycle|Otto cycle]]

:[[Rankine cycle]]

:[[Stirling engine|Stirling cycle]]

The outcome of thermodynamics is that it unveals a secret of nature (just like we saw for the Pythagoras theorem) that heat can be transformed into work.Thus, for the first time in history, man was to be released from drudgery and toil since an engine could be summoned, at will, just like an army of slaves. The Pharoes had their slaves, the Lords of the manor had their serfs but modern man has a heat engine!

What is the catch? If, perhaps, we said to our children "you can eat as much ice-cream as you want" what is the likely outcome? Most children would, I suspect, eat lots and make themselves sick. Well, it is not hard to see that we are doing the same with this new power - we are using the engine to excess and are making planet earth really sick !!!!!!!!!!!! As Vandana Shiva's book points out (page 140/ 142) - there is an evil gene in Thermodynamics. In moving from heat to work there is always an increase in Entropy, an increase in the " state of disorder". Think about fuel used in our cars; at the start is it a liquid material and, after use, it is basically a hot gas in the atmosphere never to be used again. In "slave" terms we have used our army of slaves to give us motive power and then at the end of our car journey the slaves are de-materialised never to be called upon again.

Over the millennia, nature has developed cycles of growth and decay in delicate balance and man is well on the way to destroying this balance.

Carnot cycle and the Heat Pump

The above cycle can easily traversed in a reverse manner to that of the Carnot cycle. So, the path will be a-d, then d-c followed by c-b and b-a. It is easy to see that an excess of work will have to be done on the gas. However, heat will now be transferred or "pumped" from one reservoir to another. For a refrigerator we arrange for heat to be pumped from a cold reservoir to a hot reservoir and a Heat Pump is, in essence, a refrigerator whose cold reservoir is not allowed to cool down since it has an infinite heat capacity (for instance - a flowing stream or an embedded water pipe in a lake of garden). Engines and heat pumps have similar functional diagram as shown

And instead of using efficiency (which characterises  the performance of an engine)  the Pump is specified by the so called

Coefficient of Performance (COP) where:

                                              COP = T(hot)/(T(hot) - T(cold))

If the high temperature is, say, 380 K and the low temperature is 280 K then COP = 3.8. 

The heat pump is discussed more fully in the next section.