Modern Engineering Thermodynamics

10.7 Closed System Availability Balance 329
CRITICAL THINKING
How do Eqs. (10.17) and (10.19) change for steady state processes? Does a system have to be steady state for dV/dt to be
zero? If a system is steady state, does that necessarily mean that dV/dt and dA/dt are both zero?
(a) T b > T 0 (b) T b < T 0
System boundary
at temperature T b
System boundary
at temperature T b
Q
A
Q
A
Q
A
Local surroundings
at temperature T 0
Q
A
FIGURE 10.8
(a) When T b > T 0 , the heat transfer and the associated availability transfer are both in the same direction (either both into or both out of
the system). (b) When T b < T 0 , the heat transfer and the associated availability transfer are in opposite directions.
If the system has a single heat transfer mode occurring at a constant system boundary temperature T b ,thenEqs.
(10.16) and (10.17) reduce to
1 − T
0
ð
T 1 Q 2 Þ − 1 W 2 + p 0 ðV 2 − V 1Þ − 1 I 2 = ðA 2 − A 1 Þ system = ½mða 2 − a 1 ÞŠ system (10.18)
bi
and
1 − T
0 _Q − _W + p
dV
0
T b
dt − _I =
dA
dt
system
(10.19)
Since availability represents the maximum useful reversible work that a system produces, each term in the availability
balance must have this same meaning. Note that the heat transport of availability (Eqs. (10.9) and
(10.10)) represents the maximum reversible work that a Carnot engine produces while operating between isothermal
reservoirs at temperatures T and T 0 (see Eqs. (7.9) and (7.16)). The work transport of availability
(Eq. (10.11)) corresponds to the difference between the actual work and the reversible work necessary to move
the local environment if the system changes volume during a process. The irreversible loss of available energy
associated with the actual heat and work transports of availability are contained in the irreversibility term I. This
term accounts for the difference between an actual irreversible process and a hypothetical reversible process.
Note that the availability gain can be either positive or negative (a system can gain or lose available energy during
a process), and the heat and work availability transports can also be either positive or negative. However,
Eq. (10.14) requires that the irreversibility must always be positive (I ≥ 0) because of its relation to the entropy
production and the second law of thermodynamics (i.e., S P ≥ 0).
When T b is greater than T 0 , the heat transfer and the associated availability transfer are in the same direction
(either both into or both out of the system). However, when T b is less than T 0 , they are in opposite directions.
Figure 10.8 illustrates this point and the following examples illustrate the use of this material.
EXAMPLE 10.4
A constant pressure piston-cylinder apparatus contains 1.00 kg of saturated liquid water at 120.°C. Heat is added to this system
until the contents reach a quality of 50.0%. The surface temperature of the cylinder is constant at 130.°C. Determine
the irreversibility of this process. The local environment (ground state) is at p 0 = 0.101 MPa and T 0 = 20.0°C = 293 K.
(Continued )