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.
7.7 Free Expansion of an Ideal
Gas
7.8 Entropy Change for a Liquid or
Solid
Chapter 8
Thermodynamics Potential
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
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 – yY
Then dM = dZ – Xdx – xdX –Ydy – ydY
dM = -xdX - ydY
8.3 Definition of the Thermodynamic
Potentials
8.4 The Maxwell Relations
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.
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.
8.7 Application of the Gibbs Function
to Phase Transitions
8.8 An application of the Maxwell
Relations