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Once again we use the phrase: This is where the rubber meets the road. This time it is for the calculation of the thermodynamic properties of an equilibrium chemically reacting mixture from first principles. Using some of the basic fundamentals from the previous chapter, we now heavily overlay some important results from quantum mechanics and quantum statistical mechanics, and we obtain equations from which we can directly calculate the internal energy, enthalpy, entropy, and any other thermodynamic variable for an equilibrium high-temperature gas. This is the essence of the discipline of statistical thermodynamics. These equations are the basis of modern computer subroutines that generate from scratch the equilibrium high-temperature thermodynamic properties and chemical composition used for numerical solutions of high-temperature chemically reacting flow. So this is important stuff. It is also intellectually beautiful stuff, put together by powerful minds. One of those powerful minds was that of Ludwig Boltzmann, a famous physicist and mathematician from the late 19th century. The simple inscription on Boltzmann s tombstone, given in the preceding quotation, is an equation that is the kingpin of statistical thermodynamics. You will find this equation in the middle of this chapter. The fact that it is the only inscription on the tombstone of such an important human being attests to its importance and to the importance of statistical thermodynamics in the physics of the modern world. It also attests to the reason why you should give this chapter your...