Maxwell Relation, Gibbs Free Energy, Thermal expansion

[Tian En]

By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0.

I tried but I got something funny.

My working:

 

[jim mcnamara]

This seems to be homework - please use the homework template and post the reformatted question in the homework subforum. Also your cell pone snapshot ius hard to read. We want to help, but this makes it even harder to do so. Thanks for understanding.