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Derivation of Enthalpy

Derivation of Enthalpy

Derivation of Enthalpy

(OP)
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!!

RE: Derivation of Enthalpy


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

[∂(G/T)/∂(1/T)]p = H

RE: Derivation of Enthalpy


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).  

RE: Derivation of Enthalpy

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

RE: Derivation of Enthalpy

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

RE: Derivation of Enthalpy


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.

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