I'm currently learning thermodynamics from Schroeder's "An Intoduction to Thermal Physics". He explains that in an environment of constant temperature, the system can extract heat from the environment for free when we create a system, and the Helmholtz free energy is that additional work needed that the heat did not cover. My first point of confusion- why is it certain that heat flow from the environment to the system? When we annihilate the system, why must there be heat transferred to the environment? Why not the other way around? Secondly, why is it required that the environment is at constant temperature? Lastly, why is the work done to make room for the system not accounted for? In most cases, you're creating a system that has some finite volume, so there should be a PV term. Since this is not accounted for here, what makes the Helmholtz free energy a useful quantity?