I'm reading a thermo book and I'm on the chapter dealing with the first law of thermodynamics. The book is discussing functions of state and how the internal energy is a function of state because it has a well defined value at every equilibrium state of the system. It says that the work and heat are not functions of state because if we look at a given state, we wouldn't be able to tell how the energy was added or subtracted from the heat or work in order to achieve our current total internal energy. My question is: in an adiabatic process, where Q = 0, the internal energy is just equal to the work done on the system. In this case, would work now be a function of state along with the internal energy since the work would be well defined always? Thanks!