Re: [Phys-l] T dS versus dQ

[John Denker <jsd@av8n.com>]

On 01/17/2010 11:33 PM, Bernard Cleyet wrote:

> Could one substitute a heating element instead of the speaker?  Very
> easy to measure the E in.

That depends.  
 -- If you want to do that as a separate, *additional* 
  experiment, as part of a compare-and-contrast exercise, 
  that's a good idea.
 -- If you want to do that to the exclusion of the version
  based on the sound transducer, that's not good.

The experiments discussed yesterday serve multiple 
purposes.  Getting rid of the speaker version would 
defeat some of the most interesting purposes.

For starters, one of my objectives was to demonstrate
that there are multiple mutually-inconsistent definitions
of "adiabatic" and multiple mutually-inconsistent
definitions of "heat".  If you re-arrange things so 
that only entropy that enters the gas flows across the 
heater/gas boundary, then some of the inconsistencies go 
away.  My point is that dissipative processes are part 
of the real world, and any worthwhile theory of 
thermodynamics needs to be able to account for entropy 
that is created from scratch within the interior of the 
gas, *not* flowing in across any boundary.  This means 
that the definition that defines heat and work by 
dividing dE into T dS and P dV (the "heat" term and the 
"work" term) is grossly inconsistent with the definition 
that defines heat in terms of energy flowing across a 
boundary due to a difference in temperature.

Another of my objectives was to make the point that you 
ought not take dE = T dS - P dV as an axiom or article 
of faith or "first law", because Mother Nature does not 
uphold this "law".  You use calculus to expand dE in 
terms of T dS and P dV *provided* that E can be expressed 
as a function of S and V alone ... but this simply cannot
be done when there are sound waves running around.  If
you get rid of the sound transducer, it defeats this
objective.

By way of analogy, if I ask a question about mountain-
climbing technique, I don't want an answer that says 
don't worry about it because you can always ride to 
the top of the mountain in a helicopter.  That doesn't 
answer my question;  it involves different apparatus, 
different technique, different concepts, and different 
terminology.  

By the same token, if I ask a question about irreversible
processes, I don't want an answer that says don't worry
about it, because you can always get to the same final
state using some combination of reversible processes.
That doesn't answer my question;  it involves different 
apparatus, different technique, different concepts, and 
different terminology.

Dissipative processes are part of the real world.

> p.s. one prob. students will be suspicious of using two different
> methods of adding energy?

"Suspicious" is a needlessly pejorative term.  I want
the students to be curious, inquisitive, and even 
skeptical.  I want them to compare the various methods
of adding energy.  This is no problem.  No problem
whatsoever.