Page 84 - Advanced thermodynamics for engineers

4.4 AVAILABLE AND NON-AVAILABLE ENERGY 69

and the maximum work that can be obtained by expanding to the dead state is
w max ¼ a 1 a 2 ¼ 849:5 ð 8:7Þ¼ 858:2kJ=kg
Again, this could have been evaluated using Eqn (4.12b) to give

w max ¼ Da ¼ h 1 þ v 1 p 0 p 1 h 2 þ v 2 p 0 p 2 T 0 s 1 s 2
2

¼ 3343 146:6 þ 0:1078 1 30 10 0:001006 1 1 10 2

308 7:082 0:5045
¼ 3196:4 312:6 þ 0 2025:9 ¼ 857:9kJ=kg
This shows that although the energy available in the system was 3020 kJ/kg (the internal energy) it
is not possible to convert all this energy to work. It should be noted that this ‘energy’ is itself based on a
datum of the triple point of water, but the dead state is above this value. However, even if the datum
levels were reduced to the triple point the maximum useful work would still only be
2

w max ¼ Da ¼ 3343 0 þ 0:1078 0:00612 30 10 273 7:082 0 ¼ 1086:3kJ=kg:

It is also possible to evaluate the availability of a steady-flow system and this is defined in a similar
manner to that used above, but in this case the reversible heat engine extracts energy from the flowing
stream. If the kinetic and potential energies of the flowing stream are negligible compared to the
thermal energy then the steady-flow availability is
a f ¼ h T 0 s (4.13a)
The change in steady flow availability is
Da f ¼ a f2 a f1 ¼ h 2 T 0 s 2 ðh 1 T 0 s 1 Þ (4.13b)
Thus the maximum work which could be obtained from a steady-flow system is the change in flow
availability, which for the previous example is
w max ¼ Da f ¼ ða f2 a f1 Þ¼ h 1 T 0 s 1 ðh 2 T 0 s 2 Þ
¼ð3343 146:6Þ 308 ð7:082 0:5045Þ
¼ 1170:4kJ=kg:

4.4 AVAILABLE AND NON-AVAILABLE ENERGY
If a certain portion of energy is available, then obviously another part is unavailable – the unavailable
part is that which must be thrown away. Consider Fig. 4.4; this diagram indicates an internally
reversible process from a to b. This can be considered to be made up of an infinite number of strips
1-m-n-4-1 where the temperature of energy transfer is essentially constant, i.e. T 1 ¼ T 4 ¼ T. The
energy transfer obeys
dQ dQ 0
¼
T T 0