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.


<< Home
Talk largely about energy and work, but also politics and other random thoughts

Mail Engineer-Poet

(If you're mailing a question, is it already in the FAQ?)

Important links

The Reference Library

Blogchild of

Armed and Dangerous

Blogparent of


The best prospect for our energy future:
Flibe Energy

January 1990 / February 2004 / March 2004 / June 2004 / July 2004 / August 2004 / September 2004 / October 2004 / November 2004 / December 2004 / January 2005 / February 2005 / March 2005 / April 2005 / May 2005 / June 2005 / July 2005 / August 2005 / September 2005 / October 2005 / November 2005 / December 2005 / January 2006 / February 2006 / March 2006 / April 2006 / May 2006 / June 2006 / July 2006 / August 2006 / September 2006 / October 2006 / November 2006 / December 2006 / January 2007 / February 2007 / March 2007 / April 2007 / December 2007 / January 2008 / May 2008 / June 2008 / August 2008 / October 2008 / November 2008 / December 2008 / February 2009 / March 2009 / April 2009 / May 2009 / June 2009 / July 2009 / August 2009 / September 2009 / October 2009 / November 2009 / December 2009 / January 2010 / April 2010 / May 2010 / June 2010 / July 2010 / August 2010 / September 2010 / October 2010 / November 2010 / December 2010 / January 2011 / February 2011 / March 2011 / April 2011 / May 2011 / July 2011 / August 2011 / September 2011 / October 2011 / April 2013 / November 2013 / December 2013 / January 2014 / February 2014 / March 2014 / April 2014 / July 2014 / August 2014 / September 2014 / October 2014 / November 2014 / February 2015 / April 2015 / October 2015 / March 2016 / April 2016 / May 2016 / June 2016 / July 2016 / November 2016 / December 2016 / February 2017 / May 2017 / June 2017 / September 2017 / October 2017 / November 2017 / March 2018 / May 2018 / June 2018 / October 2018 / December 2018 / January 2019 / March 2019 / June 2019 / October 2019 / November 2019 / March 2020 / June 2020 / December 2020 / March 2021 / April 2021 / May 2021 /

Powered by Blogger

RSS feed

Visits since 2006/05/11: