Strategy to Analyze Nonequilibrium Systems

Now that the basic tools are available to begin the development of the thermodynamics of irreversible processes, the overall strategy is outlined as follows  

Step 1. Use the equations of continuity and motion to develop an equation of change for kinetic energy. 

Step 2. Use the total differential of specific enthalpy in terms of its natural variables, via Legendre transformation of the internal energy from classical thermodynamics, to re-express the pressure gradient in the momentum balance in terms of enthalpy, entropy, and mass fractions. Then, write the equation of change for kinetic energy in terms of specific enthalpy and entropy. 

Step 4. Add the equations of change for internal and kinetic energies to obtain the equation of change for total energy. 

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