Mass balance entropy changes

The general entropy balance relations for a control volume are given in terms of the rate of entropy change due to the heat transfer, mass flow, and entropy production... 

In this last equation, the first term on the right-hand side is the entropy change of stream 1 from its initial temperature to the final temperature of stream 3, and the second term is the entropy change of the cold stream from its initial temperature to the exit temperature in stream 3. The entropy terms can be calculated since all temperatures are known. What is still missing is the mass flow rate of stream 2. This is obtained from the energy balance ... 

Assuming negligible kinetic and potential energy changes, mass, energy, and entropy balances yield... 

The mass energy and entropy balance equations are needed. The rate of change of probability density with time is... 

Another feature of the present theory is that it provides a formalism for deducing a complete mathematical representation of a phenomenon. Such a representation consists, typically, of (1) Balance equations for extensive properties (such as the "equations of change" for mass, energy and entropy) (2) Thermokinematic functions of state (such as pv = RT, for simple perfect gases) (3) Thermokinetic functions of state (such as the Fourier heat conduction equation = -k(T,p)VT) and (4) The auxiliary conditions (i.e., boundary and/or initial conditions). The balances are pertinent to all problems covered by the theory, although their formulation may differ from one problem to another. Any set of... 

The designation reversible arises from the following observation. Consider the change in state of a general system open to the flow of mass, heat, and work, Between two equal tiTne intervals, 0 to t and to f2, where t2 = 2t. The mass, energy, and entropy balances for this system are, from Eqs. 2.2-4, 3.1-6, and 4.1-9,... 

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. 

A uniform thermodynamic system—(uniform) body—may be visualized as a block of single (i.e., pure or one-constituent) material, the mass of which is fixed (closed system) with properties depending only on time (and not on space). Therefore, the state and state functions change only in time. Results (1.5) and (1.42) (where it is possible to use time integration) may be expressed in the rate form as it was explained at the end of Sect. 1.4. Consequently, such forms of energy balance and entropy inequality in uniform systems are [1, 3, 4]... 

Two chemically dissimilar polymers will naturally attempt to phase separate and the structure that is formed will reflect the way in which this process occurs and the driving forces associated with the process. Phase separation is used to achieve rubber toughening in thermoset resin systems. Low molar mass CTBN copolymer is soluble in the simple mixtures of monomers used to create amine-cured epoxy resins systems. However, as the molecular mass of the epoxy resin increases so the balance of entropy and enthalpy of mixing of these components changes and a driving force for phase separation is created. 

---