Maxwell and other Thermodynamic Equalities

The great painters have shown us valuable art


(the above sentence is used to build the mechanism shown below)



The temperature... Great Gibbs Free Energy... Painters pressure... Have enthalpy
Shown entropy... Us potential energy... Valuable Volume... Art Helmholtz Free Energy



Follow the arrows. Because T->V->S encounters one negative sign, write -(dT/dV)s
Because P->S->V ecounters two negative signs, write (dP/dS)V

thus 
  dt         dP

- --    =    --

  dV S       dS V
which is equal to 
  dt         dP

  --    =  - --

  dV S       dS V
which is what you see below:

Maxwell Relationships


Using the above formalism with the arrows, you should arrive at: 

-(dT/dV)S = +(dP/dS)V      +(dt/dV)S = -(dP/dS)V

+(dT/dP)S = +(dV/dS)P

+(dS/dP)T = -(dV/dT)P

-(dP/dT)V = -(dS/dV)T      +(dP/dT)V = +(dS/dV)T
I heard that some teachers don't like this because they say it doesn't have any "physical meaning." I don't worry about that--I think the point is that the existence of mechanisms like the one above shows there is an interconnectivity to the the state variables of thermodynamics. Notice also that there is quite a bit of "conceptual symmetry", for lack of a better term at this point.
  • There are the same number of T's, S's, V's, and P's.

  • There are as many minus signs as there are plus signs.

  • You should notice other signs of "conceptual symmetry." [someone email me a better term to use--please!

    Scrap Differentials (scrap for now)


    Last Update- January 5, 1995- wld