atkins’ physical chemistry eighth edition chapter 3 – lecture 2 the second law copyright © 2006...
TRANSCRIPT
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