The Second law

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Dr. F. E. Hernández
The Second law
Chapter IV
Peter Atkins, Physical Chemistry, 7th edition
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The Second
Spontaneity of physical and chemical changes
T1 gt T2
The dispersal of energy
No process is possible in which the sole result
is the absortion of heat from the reservoirr and
its complete conversion into work
State function
2nd law
Irreversible processes
DSUniv gt 0
Criteria of spontaneity ?
Perfect gas expand into vacuum and DUSys 0
DUTot 0
USys gt minimum ?
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The Entropy S
Statistical concept
Monoatomic gas
Probability!
Vi
Vf
Only chaotic-translation energy
W(vi) t Vi W(vi) W(vi) W2(Vi) WN(vi) t N
VNi
1 atom
2 atoms
S a W(v)
Entropy a W
N atoms
Extensive
S(v) a WN(v)
1/2
1/4
S(v) a lnWN(v)
WN(vi) tN VNi WN(vf) tN VNf
S(v) klnWN(v)
Since Vf gt Vi gt WN(vf) gt WN(vi)
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Gas expansion
DS Sf Si DS klnWN(vf)-lnWN(vi) DS
kln(tVf)N - ln(tVi)N
DS Nk lnVf /Vi
N nNA and R NAk
DS nRlnVf /Vi
Vf gt Vi gt DS gt 0
Thermodynamical definiton
Energy is disperse in a chaotic way
Heat
By definition !
Rev. process
Irrev. process
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Isothermal expansion of an ideal gas
At T Const DU 0
T Const
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Surrounding entropy
TSurr Const
At V Const dUSurr dqV,Surr
For adiabatic gt q 0
Independent of the trajectory
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Entropy as a state function
Carnot cycle
A ? B Th Const B ? C q 0 C ? D TC
Const D ? A q 0
Processes
qh gt 0, qC lt 0
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Efficiency of a heat engine
S DU 0
S DS 0
Sw
Sq
Since, -qc lt qh, Th gt Tc
DT ? e
http//www.bpreid.com/applets/carnotDemo.html
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Coefficient of performance (Refrigerator)
A Carnot engine that works in reverse !
For a cycle
DT ? COP
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Salvador Dali Olidamini
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The Clausius inequality
Natural process Any change
dSSys dSSurr
Clausius inequality
t
Isolated systems dqSys 0
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Variation of the entropy with the temperature
At P Const gt dqp dH if wTot wExp!
dH CpdT
Homework Th gt Tc
dq
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Entropy changes of the surrounding
Surrounding Huge reservoir
TSurr Const because CpSurr ? ?
qSurr -qSys
Adiabatic P Const.
qSurr 0 gt DSSurr 0
qp DH gt DS DH/T
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Entropy of phase transition at TTrs
At the phase transition TTrs Const
At P Const gt dqp dH if wTot wExp!
The measurements of the entropy
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Debye approximation
T ? 0 gt Cp a T3
By extrapolation we determine Cp aT3
T
0
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THE THIRD LAW
E
E
T? 0
T 0
nj
nj
Boltzmanns Distribution
(Perfect crystal)
T 369 K
S(b) ? S(a)
Thermodynamical definition (Nerst heat
theorem) DS accompanying any physical or chemical
transformation approaches zero when T ? 0
Monoclinic Orthorhombic
DS Sm(a)-Sm(b) DHTrs/TTrs
DS - 1.09 J/Kmol
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Arbitrary we can ascribe S(0) 0 _at_ T
0 (Perfect crystalline form) and S(0) gt 0 _at_ T ? 0
Measuring Cp for each state from T 0 K ? T
369 K
(DS - 1.09 J/Kmol)
Sm(a)Sm(a,0) 37 J/Kmol Sm(b)Sm(b,0) 38
J/Kmol
Third law entropies So(T) (Standard entropies)
DSTrs Sm(a,0) - Sm(b,0) - 1J/Kmol Sm(a,0) -
Sm(b,0) 0 Sm(a,0) Sm(b,0)
The system
System Lets study changes Surrounding
Thermal equlibrium TSys TSurr
According to Clausius
dqV dU dqP dH
V Const (w -PdV) P Const
Heat Transfer
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V constant
P constant
Spontaneous change criteria
S,V
U,V
S,P
H,P
Gibbs energy
Helmontz energy
System
G H - TS
A U - TS
Only defined for the system
T Const
dG dH - TdS
dA dU - TdS
(Gibbs function)
(Helmonts function)
!
dGT,P 0
dAT,V 0
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System
DSSurr
DG ? DH TDSSys DHSyslt0 DSSurr
q
System
DSSurr
DG ? DH TDSSys DHSysgt0 DSSurr
q
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In chemistry Gibbs energy is more important gt P
Const
DG DH - TDS
Maximum work
V constant
P constant
Rev. process T Const
Work done by the system (w lt 0)
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Just when wRev
P Const
Rev. Process T Const
Any other Kind of work