Modern Engineering Thermodynamics

10.6 Availability 323
WHAT IS A SYSTEM’S GROUND STATE?
The “ground state” of a system is the state of a system that has zero kinetic and potential energies and that is in thermodynamic
equilibrium with its local environment. Consequently, the local environment of a system is at the system’s groundstate.
WHAT IS THE GROUND STATE NOTATION?
Zero subscripts are used to denote the ground state and the local environment thermodynamic properties as T 0 , p 0 , V 0, v 0 , U 0 ,
u 0 , H 0 , h 0 , S 0 ,ands 0 .
10.6 AVAILABILITY
Equation (10.1) represents the maximum possible reversible work that a system could produce as it changed
states to the ground state, but it is not the maximum possible useful reversible work that could be produced. To
obtain an expression for the useful work, we must subtract the work associated with moving the local environment
as the system volume changes from its initial volume V to its final volume V 0 in the ground state. Since
the local environment is at a constant pressure p 0 , Eq. (4.26) gives the reversible moving boundary work as
Then, we can compute:
ðWÞ maximum
reversible
useful
ðWÞ reversible
moving
boundary
= ðWÞ maximum
reversible
= p 0 ðV 0 − VÞ = − p 0 ðV − V 0Þ
− ðWÞ reversible
moving
boundary
= E − E 0 + p 0 ðV − V 0Þ − T 0 ðS − S 0 Þ (10.2)
Since we are dealing with “reversible” work modes here, the maximum useful reversible work for a closed system
given by Eq. (10.2) must be the potential for some conservative force vector, and we could call this work the
energy potential (or work potential) of that force. However, the term energy potential is easily confused with the
term potential energy (the potential of the gravitational force vector) and consequently is not a good choice for
the name of this new potential. Therefore, we choose the term availability for the name of this new potential,
sincethistermissynonymouswiththeworduseful and it represents the energy available within the system to
do useful work. Figure 10.4 illustrates this new concept.
Therefore, the total availability, A, of a closed system is defined as
A ðWÞ maximum
= E − E 0 + p 0 ðV − V 0Þ − T 0 ðS − S 0 Þ
reversible
useful
= mu− ½ u 0 + p 0 ðv − v 0 Þ − T 0 ðs − s 0 Þ + V 2 /2g c + gZ/g c
Š
(10.3)
System boundary
A = W max rev − W rev moving boundary
Reversible system
Heat and moving system boundary work
to or from the local environment
(ground state)
FIGURE 10.4
Availability as the maximum, reversible, useful work that can be produced.