modelling in transport phenomena

modelling in transport phenomena - Chapter 2 The...

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Unformatted text preview: Chapter 2 The Thermodynamic Properties of Real Substances In thermodynamics, we are interested in the work and heat interactions of the system with its surroundings as it undergoes a process. These quantities can be estimated once the changes in various state functions, namely, internal energy, enthalpy, and entropy, are known. The purpose of this chapter is to develop general expressions to calculate changes in internal energy, enthalpy, and entropy. 2.1 WORK FUNCTIONS For a closed system undergoing a reversible isothermal process, integration of Eq. (1.6-8) gives Q rev = T ∆ S (2.1-1) The use of Eq. (2.1-1) in Eq. (1.5-7) leads to ∆ U = T ∆ S + W rev (2.1-2) in which the changes in kinetic and potential energies are considered negligible. Rearrangement of Eq. (2.1-2) results in − W rev = − ∆ ( U − T S ) = − ∆ A = A initial − A final (2.1-3) where the term A is called the Helmholtz energy and is de f ned by A = U − T S (2.1-4) Since U , T and S are all state functions, Helmholtz energy is a state function. It is also an extensive property. As can be seen from Eq. (2.1-3), the decrease in the Helmholtz energy indi- cates the maximum work that can be obtained from a closed system undergoing an isothermal process. The term A comes from the German word &quot;Arbeit&quot;, meaning &quot;work&quot;. For a steady-state F ow system undergoing a reversible isothermal process, combination of Eqs. (1.5-9) and (1.6-9) yields ∆ H = T ∆ S + ( W s ) rev (2.1-5) in which the changes in kinetic and potential energies are considered negligible. Rearrangement of Eq. (2.1-5) gives − ( W s ) rev = − ∆ ( H − T S ) = − ∆ G = G initial − G final (2.1-6) 11 where the term G is called the Gibbs 1 energy and is de f ned by G = H − T S (2.1-7) Since H , T and S are all state functions, Gibbs energy is a state function. It is also an extensive property. As can be seen from Eq. (2.1-6), the decrease in the Gibbs energy indicates the maximum work that can be obtained from a steady-state F ow system under isothermal conditions. Helmholtz and Gibbs energies are sometimes referred to as work functions . 2.2 THERMODYNAMIC PROPERTIES OF A SINGLE-PHASE SYSTEM 2.2.1 Fundamental Equations The f rst law of thermodynamics for a closed system is given by dU = δQ + δW (2.2-1) If the process is reversible, substitution of Eqs. (1.3-2) and (1.6-1) into Eq. (2.2-1) gives dU = T dS − P dV (2.2-2) The de f nition of enthalpy is given by H = U + P V (2.2-3) The di f erential form of Eq. (2.2-3) becomes dH = dU + P dV + V dP (2.2-4) Substitution of Eq. (2.2-2) into Eq. (2.2-4) gives dH = T dS + V dP (2.2-5) The de f nition of Helmholtz energy is given by A = U − T S (2.2-6) The di f erential form of Eq. (2.2-6) becomes dA = dU − T dS − S dT (2.2-7) Substitution of Eq. (2.2-2) into Eq. (2.2-7) gives dA = − P dV − S dT (2.2-8) The de f nition of Gibbs energy is given by G = H − T S (2.2-9) The di f erential form of Eq. (2.2-9) becomes dG = dH − T dS − S dT...
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modelling in transport phenomena - Chapter 2 The...

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