University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Entropy changes of an ideal gas
For ideal gas goes from initial conditions (P1V1T1) to final conditions (P2V2T2)
d U= d Q – d W
(first law )
For reversible process , the first law equation becomes :
d U= d Q Rev – P d V
H = U + PV ( enthalpy definition )
dH=dU+PdV+VdP
d H = d Q Rev – P d V + P d V + V d P
d Q Rev = d H – V d P
RT
dQ Re v = C P dT dP
P
dQ Re v
dP
dT
=CP
-R
P
T
T
dS = C P
( divided by T)
dT
dP
-R
T
P
Integration from initial state T1 and P1 to final state T2 and P2
T 2
DS = DS 2 - DS 1 =
òC
P
T1
P
dT
- R ln 2
P1
T
Calculate entropy change at constant pressure process
Q
C dT
DS =
=ò P
T
T
But
CP
= A + BT + CT
R
D S = R [ A + BT + CT
= R [ A ln
2
2
+ DT
+ DT
-2
-2
]
dT
T
T2
C
D 1
1
+ B (T 2 - T 1 ) + (T 22 - T 12 ) - ( - )
T 1
2
2 T 2 T1
By use mean heat capacity definition
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
T 2
C Pms º
òC
P
dT / T
T1
ln(T 2 / T 1 )
The subscript ms denote a mean value specific to entropy calculation
é
C Pms
D ù
= A + BT lm + T am T lm êC +
ú
R
(T 1T 2 ) 2 û
ë
Where Tam is arithmetic mean temperature , and Tlm is the logarithmic mean
temperature
T lm =
T 2 - T1
ln(T 2 / T 1 )