>>14286632Perfect, you know enough. I hope you know what a state function is, too. These are pressure, volume, internal energy, enthalpy, density, viscosity, and more. State functions/variables have the property that they are STRICTLY determined by the properties of a substance in equilibrium, and are PATH INDEPENDENT. That is, for a substance with 3 degrees of freedom, ANY 3-1=2 state variables fix all other variables. It's also a fact there are an infinite number of them and we may define new ones as we like (gibb's free energy, etc.)
Now, suppose we are living in 18th century Scotland and we care about the efficiency of real-life steam engines. We already know from the THEOREM that Carnot proved: "The most efficient heat engine in general is constructed of all reversible processes, and ." We are clever and use Carnot's ideas to replicate ANY reversible thermodynamic process with adiabatic and isothermal processes just like those in the ideal heat engine. Each zig-zag is vaguely like a Carnot engine, in that . Repeating this process over the entire cycle reveals .
This is wonderful news because it means we have found a NEW STATE FUNCTION! We know is a state function because it is strictly conserved over a reversible cycle. We call this new function , aka entropy. When the cycle is IRREVERSIBLE, we may then show with Carnot's theorem and the conservation of energy that must be true. This is Clausius' inequality.
