Page 18 - Entrophy Analysis in Thermal Engineering Systems

8 Entropy Analysis in Thermal Engineering Systems

To alter the entropy of a system would yield a change in the entropy of its
immediate surrounding. Let us consider the second example of Section 1.5.
The amount of heat required to increase the temperature of water from 20°
Cto60°Cis Q¼mc p ΔT¼(1)(4.18)(60 20)¼167.2 kJ. Suppose this
amount of heat is supplied from a condensing steam at 100°C. Given the
evaporation enthalpy of 2256kJ/kg for water at 100°C, about 0.074kg
steam should be condensed to provide 167.2kJ heat.
The change in the entropy of the condensing steam at the constant tem-
perature of 100°C is calculated as follows.
167:2
ΔS steam ¼ S 2 S 1 ¼ ¼ 0:448 kJ=K
373:15
The negative sign indicates that the heat is extracted from the steam. Thus,
the change in the entropy of the steam is also negative.
If we now consider the net entropy change (of the system and its sur-
rounding), we find

ΔS net ¼ ΔS water + ΔS steam ¼ 0:535 0:448 ¼ 0:087kJ=K
That is, the process of heating water from 20°Cto60°C where the source of
heat is the steam condensing at 100°C leads to a net increase of 0.087kJ/K in
entropy. This net entropy increase is referred to as the entropy generation.

1.7.1 Entropy generation in closed systems

The relation for the entropy generation of a system with a fixed mass can
now be presented by generalization of the example that we just discussed
above.
(1.12)
Φ ¼ ΔS system + ΔS surrounding
where the change in the entropies of the system and the surrounding can be
evaluated using Eq. (1.10). If the system receives heat from its surrounding,
the first term on the right-hand side of Eq. (1.12) yields a positive value,
whereas the second term leads to a negative value. Conversely, if the system
loses heat to its surrounding, the first term yields a negative value and the
second term leads to a positive value. In either case, Eq. (1.12) will always
have a positive quantity.
Eq. (1.12) may be expressed in alternative forms depending on whether
the temperature of the system or surrounding is constant. For example, if
the system receives an amount of heat Q from a heat source (the surrounding)
maintained at a constant temperature, the entropy generation is determined as