University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Evaluation of Entropy
a) At constant volume ( isomeric)
dW  0
dU  dQRev.
CV dT  TdS  S  CV ln
T2
T1
Isobaric process
dH  dQRe v.
C P dT  TdS  S  C P ln
T2
T1
b) Isothermal process
dU  0
dQRe v.  dW
TdS  PdV  S  RT ln
V2
V1
c) Adiabatic process
dQ  0  dS  0
d) Polytropic process
dU  dQRe v.  dW
CV dT  TdS  PdV
T2
V2
dT
R
TdS  CV dT  PdV  S   CV
  dV
T
V
T1
V1
S  CV ln
Heat pump
T2
V
 R ln 2
T1
V1
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Operate between the same to temperature level but direction of heat transfer are
reversible and work is required ( e.g., refrigeration cycle)
∆ U = Q net + W ( first law)
0 = QC – QH + W
W = Q H - QC 
…….
(1)
Entropy analysis
S H 
∆S
QH
TH
T otal = ∆S H
, S C  
QC
and , ∆S pump = 0
TC
+ ∆S C + ∆S pump = 0
STotal  0 
QH QC

0
TH
TC
….. (2)
 TH

 1
From equations 1 and, 2 : Wheatpump  QC 
 TC

COP 
QC
TC
outlet


W pump
inlet
TH  TC
COP :coefficient performance pump
Ex: Thermodynamic device cools small refrigerator and discards heat to the
surroundings at 298.15K .The maximum electric power to which the device is
designed is 100 W , the heat load on the refrigeration is 350 W what is the
maximum temperature that can be maintained in the refrigerator?
If Carnot engine is connected to Carnot pump (refrigerator) so that all the work
produced by engine is used by refrigerator
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Q1 is he heat rejected by Carnot engine
Q2 is the heat rejected by Carnot refrigerator
WE=WP
Engine
WP
T
WE
T
 1

1
and, pump
QH
TH
QC TC
WE = QH –Q1 and , WP = Q2 -QC

T
QH 1 
TH

T


  QC 
 1

 TC

T T
QH  H
 TH
 T  TC

  QC 

 TC
 T  TC  TH

QH  QC 
T

T
 H
 TC






Relation between QH and QC
Q  QH  QC
 TH  T
QH 
 TH
 TH  T
QH 
 TH
 T  TC

  QC 

 TC



 T  TC

  (Q  QH )

 TC
 T  TC
QH  Q
 TH  TC
 TH

T



Relation between Q H ( hot reservoir)and Q(heat sink)