Equilibrium Conditions
We introduced the second law of thermodynamics to formalize the statement that a system which is left to itself will approach a final stable equilibrium state. A system left completely to itself is isolated, and does not exchange
heat, work or mass with its surroundings, therefore Q˙ = W˙ = 0; for such a system, the second law states that in equilibrium entropy will assume a maximum. While the initial state of a system typically is inhomogeneous, in equilibrium we expect homogeneous temperatures and zero velocity, since internal heat transfer will equilibrate temperature, and internal friction will dissipate all kinetic energy. If gravity can be ignored, pressure and density (in a single phase system) are homogeneous as well, else they might be inhomogeneous, as, e.g., in the barometric formula.
Below, we shall confirm these expectations by evaluating the second law for isolated systems. Thereafter, we generalize the discussion to thermodynamic equilibria of closed systems with various boundary conditions. The state of the system can be controlled from the surroundings of the system in a number of ways. When the system is in thermal contact with a temperature reservoir it will assume the temperature of the reservoir, and thus the system temperature is controlled. The system volume can be controlled by confining material into a closed box. The system pressure can be controlled by exerting a constant force on a piston that closes the system. The system’s energy E is controlled when heat and work balance, i.e., Q˙ Systems at controlled temperatures or pressures will exchange heat or work, and change their volume, as they approach their equilibrium state.
We shall see that, depending on the boundary conditions, different thermodynamic properties will attain a minimum or a maximum in equilibrium.
However, the resulting equilibria share the same characteristics.