Page 19 - Entrophy Analysis in Thermal Engineering Systems

Fundamental concepts 9

Q
Φ ¼ S 2 S 1 T s (1.13)

where S 2 S 1 is the increase in the system entropy and T s denotes the heat
source temperature.
If the system temperature also remains constant during the process,
Eq. (1.13) becomes

Q Q
Φ ¼ T sys T s (1.14)
Eq. (1.14) is indeed a simple explanation for the generation of entropy. As
the heat flows from the surrounding (heat source) to the system, the sur-
rounding temperature should be greater than the system temperature; i.e.,
T sys <T s . From this, we have (1/T sys 1/T s )>0. Also, because Q>0, we
conclude that Q(1/T sys 1/T s )>0, and thus Φ>0.
It should be remembered that the surrounding of a system is the region at
the vicinity of the boundary of the system, which may have energy interac-
tion (work, heat, or both). If one takes the system and its surrounding as a
new system with no external interactions, the new system can be treated as
an isolated system. Hence,

Φ ¼ ΔS system > 0 (1.15)

Eq. (1.15) states that for an isolated system whose state changes from 1 to 2,
the entropy at the final state 2 will be higher than that at the initial state 1. For
example, consider a 2-kg block of carbon steel at 90°C that is dropped into a
5-L perfectly insulated container filled with water at 20°C. The system of
block+water is an isolated system, which reaches a thermal equilibrium
once the temperature of the block and the water becomes the same.
The thermal equilibrium temperature can be determined from the first
law equation, i.e., Eq. (1.4). For the system of block+water, we have

ΔU ¼ 0 ! ΔU block + ΔU water ¼ 0 ! mcðÞ T eq 90 + mcðÞ T eq 20
block water
¼ 0
Solving the equation with a specific heat of 0.49kJ/kgK for the block and
4.18kJ/kgK for the water yields T eq ¼23.14°C. The entropy generation
can now be determined using Eqs. (1.15) and (1.10).