University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Entropy
h =1-
QC
=1-
QH
Þ
QC
T
= C
QH
TH
Þ
QH
Q
= C
TH
TC
TC
TH
If used numerical value for heats , QH is positive and QC negative , lead to :
Þ
Q
Q
QH
Q
=- C Þ H + C =0
TH
TC
TH
TC
Thus for a complete cycle of a Carnot engine
As known for any cyclic process
ò
òd
Q
åT
=0
= 0 , and integration for complete cycle
dQ rev
=0
T
thus it can be concluded that
and its equal to :
dS =
dQ
or dQ rev = TdS
T
D S System = -
Q
T1
D S Surroundin gs =
Q
T2
Q
is represented a state function called Entropy S.
T
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Q Q
+
is a positive value , and for irreversible process the entropy
T1 T2
change is a positive , all spontaneous process [∆S ≥ 0 ]
D S Total = -
D S Total = -
Q Q Q (T1 - T2 )
+
=
T1 T2
T1T2
Since T1 > T2 , the total entropy changes result from this irreversible process is
positive , ∆S Total becomes smaller as the difference between T1 and T2 get
smaller.
Since entropy is a state function , the entropy change of any system and its
surroundings considered together is positive and approach zero.
Where ∆S Total = ∆S System + ∆S Surroundings ≥ 0
When a process is reversible and adiabatic dQ Rev. = 0 , thus the entropy of system
is constant .
During irreversible adiabatic process and the process is said to be isotropic
dQ rev = TdS
ò dQ
S2
rev
=
ò T dS
S1
S2
Q Re v =
ò TdS
S1
The integration represent an area under curve , in this case entropy is the lost work.
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Heat Engine
Heat engine involve a working fluid to and from which heat is transferred
® Receive heat Q from high temperature source.
® Concert part of this heat to work.
® Reject the remain with heat Q to low temperature sink.
For Carnot engine and by equating the two below equations
h =
W
Q
and h =
T1 - T 2
T1
æ
T -T2
Q (T 1 - T 2 )
T
W
= 1
ÞW =
= Q çç 1 - 2
Q
T1
T1
T1
è
ö
÷÷
ø
This is the maximum work can be got ,
During the first case , the work lost is W = ( DS Total )(T 2 )
Generally T2 is represented surroundings temperature .