Page 89 - Advanced thermodynamics for engineers

74 CHAPTER 4 AVAILABILITY AND EXERGY

T 2 p 2
Ds 12 ¼ c p ln R ln ¼ 0:6411 0:5565 ¼ 0:08639 kJ=kg K:
T 1 p 1
Hence
Da f ¼ a f2 a f1 ¼ Dh T 0 Ds
¼ 259:4 278 0:08639 ¼ 235:4kJ=kg
There has been a greater increase in availability than in the case of reversible compression. This
reflects the higher temperature achieved during irreversible compression.

(c) The change of availability of the surroundings is equal to the enthalpy change of the system, i.e.
Da surr ¼ 259.4 kJ/kg.
(d) The process an adiabatic one, i.e. there is no heat loss or addition. Hence the irreversibility of the
process is given by

I ¼ T 0 Ds ¼ 278 0:08639 ¼ 24:02 kJ=kg
This is the negative of the change of availability of the universe (system þ surroundings) which is
given by
Da univ ¼ Da system þ Da surr ¼ 235:4 259:4 ¼ 24:0kJ=kg
Hence, while the available energy in the fluid has been increased by the work done on it, the change
is less than the work done. This means that, even if the energy in the gas after compression is passed
through a reversible heat engine, it will not be possible to produce as much work as was required to
compress the gas. Hence, the quality of the energy in the universe has been reduced; even though the
quantity of energy has remained constant.

4.6 GRAPHICAL REPRESENTATION OF AVAILABLE ENERGY
AND IRREVERSIBILITY
Consider the energy transfer from a high-temperature reservoir at T H through a heat engine (not
necessarily reversible), as shown in Fig. 4.7.
The available energy flow from the hot reservoir is

E H ¼ Q H T 0 DS H (4.16)
The work done by the engine is

W ¼ Q H Q 0
The total change of entropy of the universe is

Q H Q 0
SDS ¼ DS H þ DS 0 ¼ (4.17)
T H T 0
Hence the energy which is unavailable due to irreversibility is defined by

E irrev ¼ E H W ¼ Q H T 0 DS H W
¼ Q H T 0 DS H ðQ H Q 0 Þ¼ Q 0 T 0 DS H (4.18)
¼ T 0 ðDS 0 DS H Þ