Page 14 - Entrophy Analysis in Thermal Engineering Systems

4 Entropy Analysis in Thermal Engineering Systems

Eq. (1.4) states that the change in the internal energy of a closed system in
a thermodynamic process equals the heat received by the system from an
external source minus the work performed by the system. Note that the sign
convention used in Eq. (1.4)—and throughout this book—is that the heat
transferred to the system is positive and the heat transferred from the system
to its surrounding is negative. Further, the work performed by the system on
its surrounding is negative, whereas the work done on the system is positive.
The differential form of the first law applied to a closed system is

(1.5)
dU ¼ δQ δW
where d is an exact differential, whereas δ denotes an inexact differential.
The first law equation for an open system (control volume) undergoing a
steady-state process, which can exchange mass with its surroundings through
n inlet and m outlet ports, obeys

n
m X
X
_
Q _ W ¼ _ m j h j _ m i h i + Δ _ E ke + Δ _ E pe (1.6)
j¼1 i¼1
_
_
where Q denotes the rate of heat transfer, W is the power (rate of work), h is
the specific enthalpy, Δ _ E ke denotes the difference between the kinetic ener-
gies of the outflows and inflows, and Δ _ E pe accounts for the difference
between the potential energies of the outflows and inflows.
In many thermodynamic applications, the effects of kinetic energy and
potential energy are neglected. Eq. (1.6) then reduces to

n
m X
X
_
Q _ W ¼ _ m j h j _ m i h i (1.7)
j¼1 i¼1
For an open system undergoing a transient process over a finite time, the first
law equation reads

m n
X X
Q W ¼ m j h j m i h i + ΔU (1.8)
j¼1 i¼1
In the case of no inlet flow (m i ¼0) and no outlet flow (m j ¼0), Eq. (1.8)
reduces to Eq. (1.4). For an adiabatic process (Q¼0) and in the absence
of work, the change in the energy of the system depends solely on the out-
going and incoming enthalpy flows.