Why specific heat at near critical point equals differentiate twice Gibbs energy?

[ndung200790]

Please teach me this:
Why specific heat near critical point equals differentiate twice Gibbs free energy with respect to temperature, but not differentiate once with respect to temperature as usually doing.
Thank you very much in advance.

 

[ndung200790]

I mean to differentiate twice with respect to temperature.

 

[ndung200790]

I have just found in L.E.Reichl that specific heat equals the result of differentiating twice the Gibbs free nergy(with Y,N=constant).