Question

demonstrate the importance of helmholtz Free energy concept as it relates to spontaneous processes

Answer 1

Definition of Helmholtz Free Energy

We define a new state function:
A = U -TS such that dA ≤ 0.
We call A the Helmholtz free energy.
At constant T and V the Helmholtz free energy will decrease
until all possible spontaneous processes have occurred. At
that point the system will be in equilibrium.
The condition for equilibrium is dA = 0.

and also Expressing the change in the Helmholtz free energy we have
ΔA = ΔU – TΔS
for an isothermal change from one state to another.
The condition for spontaneous change is that ΔA is less
than zero and the condition for equilibrium is that ΔA = 0.
We write
ΔA = ΔU – TΔS ≤ 0 (at constant T and V)
If ΔA is greater than zero a process is not spontaneous.
It can occur if work is done on the system, however. The
Helmholtz free energy has an important physical interpretation.
Noting the qrev = TΔS we have
ΔA = ΔU – qrev
According to the first law ΔU – qrev = wrev so
ΔA = wrev (reversible, isothermal)
A represents the maximum amount of reversible work that
can be extracted from the system.