TITLE.PM5

256 ENGINEERING THERMODYNAMICS

dharm

/M-therm/th5-3.pm5

By including any system and its surrounding within a single boundary, as shown in
Fig. 5.23, an isolated system can be formed. The combination of the system and the surroundings
within a single boundary is sometimes called the Universe. Hence, applying the principle of
increase in entropy, we get

(dS)universe (^) _≥ 0
where (dS)universe = (dS)system + (dS)surroundings.
System
temperature
Surrounding
temperature
T 0
Boundary of
the universe
Fig. 5.23. Entropy change of universe.
In the combined closed system consider that a quantity of heat δQ is transferred from the
system at temperature T to the surroundings at temperature T 0. Applying eqn. (5.24) to this
process, we can write
(dS)system > – δQ
T
(–ve sign indicates that heat is transferred from the system).
Similarly, since an amount of heat δQ is absorbed by the surroundings, for a reversible
process, we can write
(dS)surroundings =
δQ
T 0
Hence, the total change in entropy for the combined system
(dS)system + (dS)surroundings ≥ – δδQ
T
Q
T

• 0
  or (dS)universe ≥ dQ −+
  F
  HG
  I
  KJ
  11
  TT 0
  The same result can be obtained in the case of an open system.
  For both closed and open systems, we can write
  (dS)universe ≥ 0 ...(5.27)
  Eqn. (5.27) states that the process involving the interaction of a system and the surround-
  ings takes place only if the net entropy of the combined system increases or in the limit remains
  constant. Since all natural processes are irreversible, the entropy is increasing continually.