(Thermodynamics) Express Helmholtz free energy as a function of entropy and temperature

Question

fellowroot · Answer

Here is the equation. 

Helmholtz free energy

F = U - TS

or 

F = U - (delta T)S

S = systems final entropy

F = is the energy that must be provided as work if you are creating the system out of nothing. 

or

F = the energy that comes out as work, if you annihilate the system. Since you have to dump some heat, equal to TS into the environment in order to get rid of the systems entropy. 

in the end F is the available, or "free" energy. 

T = temperature.

fellowroot · Answer

and U is also energy too, but it seems to be kind of confusing because there are two different types of energy.