I am study chapter 5 of An Introduction to Thermal Physics by Schroeder and I am having trouble understanding his explanation of the differences between enthaply, Helmholtz free energy, and Gibbs free energy. Schroeder defines enthalpy of a system as its energy plus the work needed to make room for it in an environment with constant pressure P : H = U + PV. Then he explains that if the environment is one of constant temperature, the system can extract heat from its environment for free, so all that is needed to create the system from nothing is any additional work needed. (Helmholtz free energy, F is defined by F = U - TS). My main question is why can the system extract heat for free from an environment at constant temperature. Can someone explain this in more detail? Also, helmholtz free energy, unlike enthalpy, does not account for the work needed to make room for the system in the environment? Is this because Helmholtz free energy is measured when the environment is at constant temperature and not at constant pressure? So overall, is it true that the main difference between H, F, and Gibbs free energy is that Enthalpy is the energy needed to create a system out of nothing in an environment at constant pressure only. Helmholtz free energy is the energy needed to create a system out of nothing in an environment at constant temperature only. Gibbs free energy is the energy needed to create a system out of nothing in an environment at both constant pressure and constant temperature. Am I understanding this correctly? Thanks!