Is there a way to calculate the coefficient of thermal expansion (alpha) from Helmholtz free energy (A) ?

sublimnes9

sublimnes9

Answered question

2022-08-13

Is there a way to calculate the coefficient of thermal expansion ( α) from Helmholtz free energy (A) ?

Answer & Explanation

Gaige Burton

Gaige Burton

Beginner2022-08-14Added 16 answers

Kind of, in differential form we have:
d A = S d T p d V
If we Sub in:
d V = ( V T ) p d T + ( V p ) T d p
We get:
d A = S d T p [ ( V T ) p d T + ( V p ) T d p ]
So
( A T ) p = S p ( V T ) p
So:
1 V ( V T ) p = 1 p V [ S + ( A T ) p ]

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