The Ergosphere
Sunday, June 06, 2004
 

The straight dope about entropy

(This post may come across as a bit discombobulated.  It is important in its own right and really should be subject to careful refinement; unfortunately I need the explanations herein to support later posts in response to certain on-going discussions so I am writing it without the preparation I would prefer.  I fear that it may not achieve its purpose because of my inability to write exactly what I need when I need it.  If so, I will update or edit.  You Have Been Warned.)

Most everyone knows the word entropy, but few know what it means.  To the information theoretician entropy is one thing, but to the engineer it is the amount of disorder in a store or stream of energy.  Entropy can only be created, not destroyed; this means that any process which accepts or generates entropy eventually has to get rid of it.  Entropy is carried by heat (energy), so creating entropy means having to reject heat as heat rather than in some other (potentially more useful) form.  The higher the entropy, the more energy must be rejected as heat and the less can be converted to work.  Once the entropy of a stream of heat has increased sufficiently there is little you can do except dump it; nothing that operates within the laws of nature can get more out of it.

We can arbitrarily define a zero-point to the entropy of a system, but only changes in entropy really mean something.  Total entropy can only increase, and one of the major ways it increases is when heat flows between different bodies.  In thermodynamic terms S is entropy and H is enthalpy (heat), and

ΔS = ΔH/Tabs
In words, the change in entropy is the change in heat energy divided by the absolute temperature at which the change takes place; transferring heat at high temperatures changes entropy less than transferring heat at low temperatures.  Note:  all temperatures are absolute (referenced to absolute zero).  In English units entropy is stated in BTU/Rankine, and in SI units it is given in Joules/Kelvin.

What does this mean in practice?  For one thing, it means that any process which takes heat at a high temperature and lets it become heat at a lower temperature increases the entropy.  Designs which emphasize high efficiency work to prevent such things.  For instance, the purpose of reheats in a steam-cycle powerplant is to allow a higher pressure in the first boiler.  This increases the temperature at which the water boils, which in turn decreases the temperature difference between the combustion gases and the water and decreases the amount of entropy produced in the heat transfer.  Feedwater heaters work similarly; they take partially-spent steam (at a lower temperature) out of the stream going through the turbines and use it to pre-heat the water going to the boilers.  This both cuts the heat rejected at the condenser ("recycling" it) and decreases the entropy produced by decreasing the temperature difference between the water being heated and the heat being supplied to do the job.  The smaller the temperature drop during heat flow, the less entropy is produced and the more energy can be converted to useful forms.

(Entropy can be created by other processes, such as by throttling a stream of fluid from a high pressure to a lower pressure.  I am not trying to give an exhaustive list here.)

When you look at delta-entropy as ΔS = ΔH/Tabs, a lot of things that look efficient on the surface are revealed as being horribly sub-optimal.  Take the gold standard of home heating, the condensing gas furnace.  Some condensing furnaces exhaust a stream of humid flue gas that is barely warm, and boast annual fuel utilization efficiencies (AFUEs) of up to 98%.  This sounds really great until you realize that the gas flame inside the furnace may be at 2000 Kelvin while the heated air leaving the unit to the house might be at 350 K or less.  The entropy of the gases (heated air and flue gas) leaving the unit is almost six times as great as the entropy of the hot combustion gas just leaving the flame zone.  Phrased another way, a large fraction of the energy of the gas could be made to do something else useful before it went to heat air.  What kind of things might be useful will be outlined in future posts.

All of the high-efficiency energy generation systems work by keeping entropy increases to a minimum.  The combined-cycle system generates the heat in an internal combustion engine (gas turbine) operating at very high temperature; the exhaust from the gas turbine is still hot and boils water to operate a steam turbine, taking a second crack at the heat.  Fuel cells work on a different principle, beginning by avoiding the entropy increases inherent in combustion itself and using the chemical combination of fuel with oxidizer to maintain a concentration gradient of chemical species which drives the migration of ions through an electrolyte (the concept of Gibbs free energy becomes important here).  Some fuel cells (like molten-carbonate fuel cells and solid-oxide fuel cells) run at temperatures high enough that their waste gas can itself drive a gas turbine, whose waste heat can in turn generate steam for a steam turbine.  Total efficiency for such a "triple threat" system might top 80%, and it all works by careful management of entropy. 

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