Derivation of Enthalpy

[jrv24]

Having difficulty deriving the following

(d(G/T))/(d(1/T) is apparently equal to H? ( G, Gibbs Free Energy, T, Temperature , H, Enthalpy - referring to partial differential keeping V constant)

How is this so? Any help would be helpful!!

 

[25362]

Since [[∂](G/T)/[∂]T]_p = - H/T², it follows that

[[∂](G/T)/[∂](1/T)]_p = H

 

[25362]

In a similar manner with the Helmholtz free energy A

Since [?(A/T)/?T]_v = - U/T², it follows that

[?(A/T)/?(1/T)]_v = U

where U is the internal energy, v is volume, and p is pressure (previous posting).

 

[chicopee]

25362, you have skipped a few details, however, I am more interested the greek symbols that you used. How did you do that?

 

[chicopee]

jrv24, I'll do one of the gibbs functions but bear in mind that I have not mastered greek symbols in this environment ,so I'll use regular letters and I'll use specific variables,ie.,v=V/m,s=S/m,etc..

With Hemlholz function
a=u-Ts>a/T=u/T-s>d(a/T)=d(u/T)-ds

(skipped a few steps) d(a/T) =du/T-udT/T^2-ds

since ds=du/T+Pdv/T
d(a/T)= -udT/T^2-Pdv/T
let v=constant
d(a/T)=-udT/T^2
since d(1/T)=-dT/T^2
d(a/t)/d(1/T)=u

 

[25362]

To jrv24, this is conventional information appearing in books on thermodynamics. You may see from the above messages that the definition you are seeking is not true.

To chicopee, use the Process TGML Step 2 option when writing a message.