7.6 entropy change in irreversible processes
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7.6 Entropy Change in Irreversible Processes. - PowerPoint PPT PresentationTRANSCRIPT
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7.6 Entropy Change in Irreversible Processes
• It is not possible to calculate the entropy change ΔS = SB - SA for an irreversible process between A and B, by integrating dq / T, the ratio of the heat increment over the temperature, along the actual irreversible path A-B characterizing the process.
• However, since the entropy is a state function, the entropy change ΔS does not depend on the path chosen.The calculation of an irreversible process can be carried out via transferring the process into many reversible ones:
• Three examples will be discussed here: (1) heat exchange between two metal blocks with different temperatures; (2) Water cooling from 90 to a room temperature; (2) A falling object.
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7.7 Free Expansion of an Ideal Gas
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7.8 Entropy Change for a Liquid or Solid
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Thermodynamics Potential
Chapter 8
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8.1 Introduction• Thermodynamic potentials: Helmholtz function F and the
Gibbs function G.• The enthalpy, Helmholtz function and Gibbs functions are all
related to the internal energy and can be derived with a procedure known as Legendre differential transformation.
• The combined first and second laws read dU = Tds – PdV where T and S, and -P and V are said to be canonically
conjugate pairs.• By assuming U = U(S,V), one has
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8.2 The Legendre Transformation• Consider a function Z = Z(x, y), the differential
equation is dZ = Xdx + Ydy where X and x, Y and y are by definition canonically
conjugate pairs.• We wish to replace (x, y) by (X, Y) as independent
variables. This can be achieved via transforming the function Z(x,y) into a function M(X,Y).
• Assume M(X,Y) = Z(x,y) – xX – yYThen dM = dZ – Xdx – xdX –Ydy – ydY
dM = -xdX - ydY
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8.3 Definition of the Thermodynamic Potentials
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8.4 The Maxwell Relations
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8.5 The Helmholtz Function
• The change in internal energy is the heat flow in an isochoric reversible process.
• The change in enthalpy H is the heat flow in an isobaric reversible process.
• The change in the Helmholtz function in an isothermal reversible process is the work done on or by the system.
• The decrease in F equals the maximum energy that can be made available for work.
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8.6 The Gibbs Function• Based on the second law of thermodynamics dQ ≤ T∆S with dQ = ∆U + P ∆V• Combine the above expressions ∆U + P ∆V ≤ T∆S ∆U + P ∆V - T∆S ≤ 0• Since G = U + PV –TS (∆G)T,P≤ 0 at constant T and P or G f ≤ Gi
• Gibbs function decreases in a process until a minimum is reach, i.e. equilibrium point.
• Note that T and P need not to be constant throughout the process, they only need to have the same initial and final values.
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8.7 Application of the Gibbs Function to Phase Transitions
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8.8 An application of the Maxwell Relations