INTRO to Diagram 4 …. When a gas is compressed so very slowly that there is a zero temperature rise, the power input is called the Work Done component (WD). The same gas compressed very quickly has a considerable temperature rise. Power input is now called Adiabatic which has TWO components called WD & Internal Energy (IE). Thermodynamics scholars have no explanation for this behaviour and call it CHAOTIC COMPRESSION.
Gas has a secret that delivers its own "free lunch" of value 2IE every full cycle. Diagrams A and B show the difference between Chaos and Order for Argon at an initial temperature and pressure of 1 atm and 300o K. Compression index l = 1.66 = (WD+IE)/IE.