ThermoReview

7/30/2019 ThermoReview

1/15

Lecture 2: Thermodynamic Review 1

Lecutre 2: Brief Review of Thermodynamics

Review of Equilibrium Thermodynamics:Equilibrium

Entropy

Solution Thermodynamics

Equilibrium Phase Diagrams

Activity and Activity Coefficients


2/15


Entropy

Entropy is a state function because the level of disorder of a system only depends on the

current condition of the system. Consequently, the entropy change for any process joining

the same two states is the same, whether the process is reversible or not.

To calculate the entropy change for any process we just find a reversible path

connecting the two states and calculate its change in entropy using the above

formula.

QT

rev Sa Sb


3/15


The Second Law

The Second Law: The entropy of the universe increases for all processes except reversible

ones, for which there is no change in Suniv.

Once disorder is created, it cannot be destroyed.

QT

Rev

Suniv 0

Suniv Ssys Ssurr

The changes in entropy of the system and surroundings

are balanced for a reversible process. That is entropy

is only transferred, and the original state of the universe

can be obtained by reversing the process.

If a process is not reversible, entropy is created and the disorder of theuniverse is increased. The entropy of the universe can never decrease.


4/15


Entropy

Entropy is a measure of the disorderin a system.

QT

rev

S

Note that for a given process, the larger the heat flow the greater the increase in S.

Also, that a given heat flow of a process causes a larger change in S at lower Ts.

Also note that if a reversible process is adiabatic, it is isentropic.

Gas

M

Heat Q

Work W

Slowly remove mass

Gas

M

Heat Q

Work W

Q

TRe v S

Isothermal Adiabatic

Q

Trev S


5/15


Criteria for Equilibrium

for irreversible processes

for reversible processes

never

Suniv 0

Suniv 0

Suniv 0

Irreversible

processes are also

called spontaneousornatural

Ssys

Ssurr

Ssys Screated Stransferre

Definitions:

A chemical system is any system made up of one or more elements.

Aphase is any distinguishable region of a chemical system which is in a well-defined state of internal

equilibrium. Phases can be open orclosed depending on whether they change or do not change theamount of material in the phase, respectively.

A component is any independently variable chemical species of the system: For example, P in Si,

(C2H5)OH in H2O.


6/15


Equilibrium

In a system that is in internal equilibrium, any infinitesimal

process about a point of equilibrium is reversible.

An infinitesimal change in the

system introduces no finite

driving forces and thus no

dissipative processes.

Examples of reversible and irreversible processes: Heat flow down a temperature gradient

Mixing of NaCl in water

Melting of ice in a glass of water at 273K

Separation of oil and water

For an infinitesimal, reversible process performed on a single-phase closed chemical system

in internal equilibrium we can write:

dU Q W

Q TdS W PdVFrom our definition

of entropyIn a chemical system

only mechanical work

is done.

dU TdS PdV i dnii


7/15Lecture 2: Thermodynamic Review 7

Equilibrium Conditions

Consider an isolated chemical system (dV=0, dU=0 and dN=0)

of two phases:

Since the system is isolated, the total volume, internal energy and

number of particles is constant. So any change in these quantities for

one phase must bebalanced by an equal and opposite change in the

other phase.

dV 0 dV dV

dU 0 dU dU

dn 0 dn dn dU dU dU

dU TdS PdV i

dni

i

dS dS dS

dS

1

T

dU

P

T

dV

i

T

dni

i

dS

1

T

dU

P

T

dV

i

T

dni

i

dV dV dV

dni dni dni

Rearranging:

For phase alpha:

Likewise:


8/15



Conditions for Phase Stability

U TS PV inii

G U TS PV

G TS PV inii TS PV

G inii

dU TdS PdV idnii

Integrate dU

From the definition of G (2nd order

Legendre transform of U)

Substituting U into our expressionfor G

Gives the Gibbs Free Energy in terms

of chemical potentials and concentrations.



The Gibbs-Duhem Equation

G i nii

dG d i nii

dG nidii idni

i

Starting with our expressions for

the Gibbs free energy

We consider how it changes foran infinitesimal process

We see that G changes because the

amount of components changes or

because the chemical potential of the

components changes

GUTS PV

dG SdT VdP i dnii

dG dU d TS d PV

Since these two expressions for dG are equivalent we can equate them to find:

SdT VdP nidii 0

The Gibbs-Duhem Equation

which relates T, P and at

equilibrium in a single phase

system

G changes because T changes

or P changes or because thecomposition changes



Gibbs Phase Rule

Each phase of a system in internal equilibrium is governed by its own Gibbs-Duhem equation:

SdT VdP nidii 0

Each phase is described by C+2 intensive variables:

T, P and the C chemical potentials.

Since the Gibbs-Duhem expression relates these C+2 variables within each phase,

only C+1 of them are independent.

If phases are in equilibrium with each other, then we have only one T and one P for

all the phases, so we still have C+2 variables. However, we now have relationships

between the C+2 variables since we have a Gibbs-Duhem expression for each phase.

f C 2

One can independently vary f intensive variables for a system

of C components and still keep phases in equilibrium.

Gibbs Phase Rule:Note: F is the number of degrees

of freedom and P is the number of

equilibrium phases.



Systems at Constant P and T

For systems at constant pressure and temperature, equilibrium is established when the

system has minimized its Gibbs Free Energy:

dG SdT VdP idnii

G

P

Slope: V

vap liq

Since a closed system at constant T and P

will minimize its Gibbs free energy at

equilibrium, we determine what equilibrium

phase a material will be in at different conditions

by determining which phase has the lowest G.

G

T

Slope: -S

liq vap

The material follows the lowest G curve,

switching from one to another at transition

points.


13/15


Phase Diagrams

Gv(T,P)

P

T

If we consider both changes in T and P, the

material follows the lowest G surface,switching from one to another at transition

points on a coexistence curve, which is

defined as the intersection of the two Gibbs

free energy surfaces. coexistence curve

Gl(T,P)

P

T

liq

vap

sol

Triple point

Critical point


14/15


Construction of a Eutectic Phase Diagram

GM

0

G' A0

GA

GB

G' B0

XB

T

1

0 XB 1

+

+L

L

+L

L

GM

0

G' A0

GA

GB

G' B0

XB 1

L

GM

0

G' A0

GAGB

G' B0

XB 1

L

GM

0

G' A0

GA

G' B0

XB

1

L

GM

0

G' A0

G' B0

XB 1

at TM(A)at TM(B)

Above TE and below

melting pointsat TEBelow TE


15/15


Vapor Liquid Equilibrium

T

0 XB 1

V

L

The equilibrium phase diagram for a vapor-liquid binary system often takes

The form of a lens diagram. The two-phase region is defined by bubble

point and dew point lines which give the compositions of the liquid and vaporin equilibrium at a particular temperature. The difference between these

compositions provides the driving force for several types of separations methods.

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