Page 20 - Entrophy Analysis in Thermal Engineering Systems

10 Entropy Analysis in Thermal Engineering Systems

Z Z
T eq
dT T eq dT
Φ ¼ ΔS block + ΔS water ¼ mcðÞ + mcðÞ
block water
90 + 273:15 T 20 + 273:15 T
23:14 + 273:15 23:14 + 273:15
¼ 2ðÞ 0:49Þ ln +5ðÞ 4:18Þ ln
ð
ð
90 + 273:15 20 + 273:15
¼ 0:023kJ=K
1.7.2 Entropy generation in open systems

For an open system with n inlet and m outlet ports that undergoes a steady-
state operation, the rate of entropy generation is determined using
Eq. (1.16).
X _ X X
m
n
_
Φ + Q ¼ _ m j s j _ m i s i (1.16)
j¼1 i¼1
T k
k
where the second term on the left-hand side of Eq. (1.16) accounts for the
net change in the entropy of the surroundings [9], and _ms is the entropy rate
crossing the system boundary due to the mass flow.
For example, in a nonmixed adiabatic heat exchanger with one hot fluid
and one cold fluid, Eq. (1.16) reduces to

_
ð
Φ ¼ _m h s h,o + _m c s c,o Þ _m h s h,i + _m c s c,i Þ
ð
(1.17)
ð
¼ _m c s c,o s c,i Þ + _m h s h,o s h,i Þ
ð
where the subscripts h, c, i, o denote hot, cold, inlet, and outlet, respectively.
1.8 Combined first and second laws

The first analytical expression for the combined first and second laws
was given by Clausius [3]. It can be obtained by eliminating δQ between
Eqs. (1.5) and (1.9). Hence,

(1.18)
dU ¼ TdS δW
For a compressible fluid, if the work done is due to the fluid pressure only,
the infinitesimal work can be represented by δW¼pdV where p represents
the pressure and V the volume, and Eq. (1.18) is rewritten as follows.
(1.19)
dU ¼ TdS pdV