Re: [Phys-l] entropy and electric motors

[John Denker <jsd@av8n.com>]

On 05/24/2008 11:34 AM, kyle forinash wrote:

> let me see if I can re-phrase my question.
>
> 1. OK, heat engines are not 100% efficient because entropy change in the 
> hot reservoir must be compensated for by entropy change in the cold 
> reservoir; 

Exactly so.

> 2. Batteries (fuel cells, etc.) additionally have entropy changes 
> related to chemical potential. So (I'm a little fuzzy on the exact 
> calculation but) again tracking the entropy of the chemicals before and 
> after they react in the battery we can say that we won't get all of the 
> energy out in a useful form because entropy has to increase (or remain 
> constant at best).

That's exactly correct as stated, and I have nothing to add concerning 
that step of the argument......

However, I will take this opportunity to mention that oftentimes
people mess up the /next/ step of the argument.  Links in the
chain of faulty reasoning include:
 -- Greatly overestimating the amount of entropy involved, and
 -- Being confused about the so-called "heat of reaction".
  (I was confused about this for years and years.)

It is very common for people to speak of "heat of reaction", denoted ΔH.
I get 170,000 hits from
  http://www.google.com/search?q=heat-of-reaction

That's a misnomer.  It's the worst sort of misnomer, because it leads
directly to a misconception.  It is hardly surprising that some people
think "heat of reaction" is necessarily related to heat.  The problem
is, it is not!  The H in ΔH does not stand for heat;  it stands for
enthalpy!  You should never think (or speak) of the heat of reaction;  
you should be thinking in terms of the enthalpy of reaction.

Alas I get only 57,000 hits from
  http://www.google.com/search?q=enthalpy-of-reaction

The confusion between heat of reaction and enthalpy of reaction is
exacerbated by the fact that in 99+% of the experiments that people
do in introductory chemistry courses, the enthalpy of reaction is
instantly thermalized, so in these examples ΔH actually shows up
as heat.  However, batteries are a hugely important counterexample.  
In normal operation, nearly all of the enthalpy of reaction shows 
up as electrical energy, not as heat.

Let's be clear:  the ΔS associated with an electrochemical reaction
is not ΔH/T ... not anywhere close.

Here's one way of looking at it:  Consider the contrast:
 *) Suppose you short-circuit a battery. It runs down and gets warm.  
  You then run a heat engine between the warm dead battery and room 
  temperature.  The Carnot efficiency will be awful.  
 *) Suppose instead that you use the battery to heat up some tiny
  resistor, perhaps the filament of a light bulb or something 
  even tinier.  It gets very, very hot.  You run a heat engine
  between the hot resistor and room temperature.  The Carnot
  efficiency will be pretty good, because of the large ΔT.

So the question is, how hot does the resistor have to be before 
the Johnson noise power that it radiates backwards into the battery 
overwhelms the DC electrical power coming from the battery?  Answer:  
reeeeally hot.  Therefore the battery-powered heat engine can have 
a very good Carnot efficiency.

   (A battery-powered electric motor achieves the same efficient
   result by a simpler method.)


Here's another way of looking at it:	Compare the left side and
right side of the figure here:
  http://www.av8n.com/physics/thermo-laws.htm#sec-metastable-t

As I've drawn it, there is zero entropy difference between the charged
state and the discharged state.  For an ideal capacitor, this is
exactly true.  For a real-world capacitor, it is AFAIK true for all
practical purposes.  For a real-world battery, ΔS is nonzero, but
it is very very small on the scale of ΔH/T.

Remember:  A battery is not a heat bath.  A heat bath is internally
in thermal equilibrium, but a battery is not.

===================

I'm not sure this answers the question ... but I figured I should
throw it out there, since these are issues that are confusing for a 
lot of people