When evaluating the entropy transfer between an extended system and the
surroundings, the boundary temperature of the extended system is simply
taken to be the environment temperature.
Closed Systems
A closed system involves no mass flow across its boundaries, and its
entropy change is simply the difference between the initial and final
entropies of the system. The entropy changeof a closed system is due to the
entropy transfer accompanying heat transfer and the entropy generation
within the system boundaries. Taking the positive direction of heat transfer
to be tothe system, the general entropy balance relation (Eq. 7–76) can be
expressed for a closed system as
Closed system: (7–79)
The entropy balance relation above can be stated as:
The entropy change of a closed system during a process is equal to the sum
of the net entropy transferred through the system boundary by heat transfer
and the entropy generated within the system boundaries.For an adiabatic process(Q0), the entropy transfer term in the above
relation drops out and the entropy change of the closed system becomes
equal to the entropy generation within the system boundaries. That is,
Adiabatic closed system: (7–80)
Noting that any closed system and its surroundings can be treated as an adi-
abatic system and the total entropy change of a system is equal to the sum
of the entropy changes of its parts, the entropy balance for a closed system
and its surroundings can be written as
System Surroundings: (7–81)
where Ssystemm(s 2 s 1 ) and the entropy change of the surroundings can
be determined from SsurrQsurr/Tsurrif its temperature is constant. At ini-
tial stages of studying entropy and entropy transfer, it is more instructive to
start with the general form of the entropy balance (Eq. 7–76) and to sim-
plify it for the problem under consideration. The specific relations above are
convenient to use after a certain degree of intuitive understanding of the
material is achieved.
Control Volumes
The entropy balance relations for control volumes differ from those for
closed systems in that they involve one more mechanism of entropy
exchange:mass flow across the boundaries. As mentioned earlier, mass pos-
sesses entropy as well as energy, and the amounts of these two extensive
properties are proportional to the amount of mass (Fig. 7–63).
Taking the positive direction of heat transfer to be tothe system, the gen-
eral entropy balance relations (Eqs. 7–76 and 7–77) can be expressed for
control volumes as
a (7–82)Qk
TkamisiameseSgen 1 S 2 S 12 CV¬¬ 1 kJ>K 2
Sgena¢S¢Ssystem¢SsurroundingsSgen¢Sadiabatic systemaQk
TkSgen¢SsystemS 2 S 1 ¬¬ 1 kJ>K 2
Chapter 7 | 381SurroundingsControl
volumemi
sime
seEntropy
transfer
by heatEntropy
transfer
by mass∆SCV =Q
T{+ misi – m{ese + SgenTQFIGURE 7–63
The entropy of a control volume
changes as a result of mass flow as
well as heat transfer.