mt 306 01 equilibrium

8/13/2019 MT 306 01 Equilibrium

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Thermodynamics and Phase diagram


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capo regime

G

H

S

Dominate G at low temperatures Dominate G at High temperatures


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Phase: Portion of the system whose properties and composition are

homogeneous and which is physically distinct from other parts of the

system phase is a region of material that is chemically uniform,

physically distinct, and (often) mechanically separable

Components: are the different element or chemical compounds which

make up the system


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Relative stability of a system is determined by Gibbs free energy (G)

TSHG

Enthalpy Absolute temperature

Entropy

Entropy is a measure of randomness of the system (or degree of

irreversibility of the process)

Enthalpy is a measure of the heat content of the system

Gibbs free energy (G)


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PVEH

Internal EnergyPressure

Volume

(K.E. + P.E. of the system)

Atomic vibrations (Liquid and Solid), or

Translational and rotational energiesof atoms or molecules within a liquid and gas

Interaction/bonds between atoms

Enthalpy


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A system is said to be in equilibrium when it is in the most stable state

Shows no desire to changead infinitum

At constant temperature and pressure a closed system (fixedmass and composition) will be in stable equilibrium if

0dG

Gibbs freeenergy G

dG = 0

Equilibrium


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Necessary criterion for phase transformation

012

GGG

Gibbs freeenergy G

State of system1 2

G1

G2

dG=0

dG=0

Metastable equilibrium Stable equilibrium

G1> G2

Equilibrium cont..dG=0


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Single component systems (pure element or molecule)

Time

TM

Liquid

Solid

Phase transformation at

constant temperature

Temperature

Time-Temperature curve


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Enthalpy and Entropy as afunction of temperature

Pp T

HC

T

pdTCH298

P

p

T

S

T

C

T

pdT

T

CS

0

H = 0 for pure element in itsmost stable state at 25oC

Quantity of heat required to

raise the temp. of thesubstance by 1 K


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VdPSdTdG

@ constant pressure

ST

G

p

Gibbs free energy as a function of temperature

System of fixed mass and composition

Varying pressure and temperature


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Variation of G withtemperature forthe solid and liquid

phases of a puremetal Latent heat

SL > Ss

HL> HS@ all temps.


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Effect of pressure on equilibrium phase diagram for pure iron

hcp

VT

H

dT

dP

eqeq

Clausius-Clapeyron Equation

0

mm VVV

0

HHH

dP/dT is negative


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Driving force for solidification

mT

TLG


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Binary solutions

Ideal solutions

Regular solutions

Real solutions


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Gibbs free energy of binary solutions

Depends on

PressureTemperature

Composition

Usually treated constant (1 atm.) in

solid state transformations

Two variables

Gibbs free energy of pure A

Gibbs free energy of binary solutions of A and B elements

Gibbs free energy of pure B+

Gibb f f bi l i


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Step 1 Step 2

Gibbs free energy of binary solutions

Mix


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BBAA GXGXG 1

Step 1

mixGGG

12


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After step 2, Gmix??

mixmixmix STHG

Step 2 - Mixing

Ideal solutions

Regular solutions

Real solutions

mixG will depend on definition of binary solution

mt 306 01 equilibrium

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