Page 16 - Entrophy Analysis in Thermal Engineering Systems

6 Entropy Analysis in Thermal Engineering Systems

2
Z
δQ
S 2 S 1 ¼ (1.10)
1 T
rev
Either of Eqs. (1.9) and (1.10) is the quantitative definition of entropy [5].
For example, the amount of heat required to evaporate 1kg of water at 100°
C is 2256kJ. The change in the entropy of 1kg of saturated liquid water
undergoing an evaporation process at 100°C is calculated as follows.

2
Z
2256 kJðÞ
δQ Q
S 2 S 1 ¼ ¼ ¼ ¼ 6:046 kJ=K
1 T T 373:15 KðÞ
rev
where S 1 is the entropy of liquid water and S 2 denotes the entropy of water
vapor at 100°C. The specific entropy of saturated liquid water at 100°Cis
1.307kJ/kgK. So, the entropy of 1kg of saturated water vapor is determined
as

ð
S 2 ¼ 1kgð Þ 1:307 kJ=kgKÞ +6:046 ¼ 7:353kJ=K
This result can be verified using thermodynamic tables or a property soft-
ware. In the example, the water temperature was constant throughout
the process. Often, the temperature varies along the process and the integral
in Eq. (1.10) is evaluated using analytical or numerical integration tech-
niques. For instance, the change in the entropy of 1kg of water at atmo-
spheric pressure whose temperature increases from 20°Cto60°Cis
determined as follows.
Use δQ¼mc p dT in Eq. (1.10) and perform integration between 293.15
and 333.15K assuming a specific heat of 4.18kJ/kgK for water. The change
in the entropy of the water is thus obtained as

Z
T 2 333:15
T 2
mc p dT
ð
S 2 S 1 ¼ ¼ mc p ln ¼ 1ðÞ 4:18Þ ln ¼ 0:535 kJ=K
T 1 293:15
T
T 1
A subtle but important note from the preceding two examples is that the
change in the entropy of a system (e.g., water in the above examples) is
determined assuming that the heat transfer takes place reversibly. It should also
be noted that we used Eq. (1.10) to determine the change in the entropy of
water only without regard to the heat source as the immediate surrounding
of the system.
In a like manner, one may also calculate the change in the entropy of the
surrounding that provided heat to the water—see Section 1.7. Moreover, it
can be deduced from Eq. (1.10) that the entropy of system will increase if it