Atkins’ Physical ChemistryEighth Edition

Chapter 3 – Lecture 2The Second Law

Copyright © 2006 by Peter Atkins and Julio de Paula

Peter Atkins • Julio de Paula

Entropy Changes Accompanying Specific Processes

(a) Expansion, isothermally from Vi to Vf:

• ΔS path-independent, so ΔS of the system is same forreversible and irreversible process

• Logarithmic dependence of ΔS shown in Fig 3.12

i

f

V

V lnnR ΔS

Fig 3.12

Logarithmic increase

in entropy of a perfect gas

expanding isothermally

i

fsys V

VlnnR ΔS

Reversible or irreversible

Entropy Changes Accompanying Specific Processes

(b) Phase changes

• Entropy increases with the freedom of motion of molecules:

S(g) >> S(l) > S(s)

• Recall that T does not change during a phase transition

• So:trs

trstrs T

HΔΔS

Trouton’s rule – wide range of liquidshave approximately the same ΔSvap

qvap = ΔHvap = Tb ∙ (85 J K-1 mol-1)

Entropy Changes Accompanying Specific Processes

(c) Heating

• From:

• At constant pressure:

• Gives:

f

i

rev

T

dqSΔ

f

i

revif T

dq)T(S)T(S

PP T

HC

i

fPi

f

i

Pi

f

i

Pif T

TlnC)T(S

T

dTC)T(S

T

dTC)T(S)T(S

Fig 3.13

Logarithmic increase

in entropy of a substance

heated at constant volume

i

fVif T

TlnC)T(S)T(S

Entropy Changes Accompanying Specific Processes

(d) Measurement of entropy for phase changes

• Entropy of a system increases from S = 0 at T = 0to some final S at T

Heating curve for water

Indicates changes when 1.00 mol H2O is heated from 25°C to 125°C at constant P

Entropy Changes Accompanying Specific Processes

(d) Measurement of entropy for phase changes

• Entropy of a system increases from S = 0 at T = 0to some final S at T

• Evaluate integrals and include ΔHtrs

• Integrals may be evaluate graphically

T

T

P

b

vapT

T

P

f

fus

T

0

P

b

b

f

f

T

(g)C

T

HΔ

T

(l)C

T

HΔ

T

(s)CS(0)S(T)

Fig 3.14(a) Variation of Cp/T with temperature of a substance

e.g., area under Solid regionof the curve is:

For S(0) use Debyeapproximation:

CP ∝ T3 at low temperatures

Then CP = aT3

fT

0

Pf T

(s)CS(0))S(T

Fig 3.14(b) Calculation of entropy from heat capacity data

The entropy for each region =the area under each uppercurve up to the correspondingtemperature Ttrs plus the entropyof each phase transition passed

T

T

P

b

vapT

T

P

f

fus

T

0

P

b

b

f

f

T

(g)C

T

HΔ

T

(l)C

T

HΔ

T

(s)CS(0)S(T)

The Third Law of Thermodynamics

• At T = 0 all thermal motion has been quenched

• In a perfect crystal all particles are arranged uniformly

• This perfection suggests that S(0) = 0

• Nernst heat theorem:

ΔS → 0 as T → 0 provided that the substance is perfectlycrystalline

3rd Law: The entropy of all perfectly crystalline substances is zero at T = 0

The Third Law Entropies

• Third law definition is a matter of convenience

• Sets a standard for relative entropies at other T

• Standard reaction enthalpies used analogously to ΔHf

• may be found in Table 3.3

tstanreac

om

products

om

orxn nSmSS

omS