Modern Engineering Thermodynamics

10.8 Flow Availability 331
EXAMPLE 10.5
A small room has a single 100. W lightbulb hanging from the ceiling. The walls are not insulated, so a steady state condition
is reached where the room walls are at 24.0°C. Determine the irreversibility rate within the room. The local environment
(ground state) outside the room is at p 0 = 0.101 MPa and T 0 = 15.0°C.
Solution
First, draw a sketch of the system (Figure 10.10).
100. W lightbulb T room = 24.0°C Ground state:
T 0 = 15.0°
p 0 = 0.101 MPA
FIGURE 10.10
Example 10.5.
The unknown is the irreversibility rate within the room. The irreversibility rate for this closed system can be determined
from Eq. (10.19) as
_I = 1 − T
0
dV
_Q − _W + p 0
T b
dt − dA
dt
In this problem, the system has a fixed volume so dV/dt = 0, and since the system is steady state, we also have (dA/dt) system = 0.
The energy rate balance applied to this closed system tells us that _Q = _W = 100 W: Then, Eq. (10.19) gives
system
15:0 + 273 K
_I = 1 − ð−100 WÞ − ð−100 WÞ + p 0 ð0Þ − 0 = 97:0W
24:0 + 273 K
Note that, of the 100. W that enters the room as electrical power, only 3% remains as available energy.
Exercises
13. Suppose the local environment (ground state) temperature in Example 10.5 is lowered from 15.0°C to 0.00°C.
Determine the irreversibility rate within the room assuming all the other variables remain unchanged.
Answer: _I = 91:9W.
14. If we change the system in Example 10.5 from the room to the lightbulb itself, then the boundary temperature increases
from 24.0°C to 40.0°C. Assuming all other variables remain unchanged, determine the irreversibility rate of the
lightbulb. Answer: _I = 92:0W
15. The basal metabolic rate of the human body is about 400. Btu/h. This means that the body gives off this much heat, or
_Q body = −400: Btu/h, when it is resting (i.e., when _W body = 0). Suppose the human body is a reversible ð_I = 0Þ closed
system with a surface boundary temperature of 98.6°F in an environment with a temperature of 70.0°F. What is the rate
of change of total availability of the human body? Answer: (dA/dt) body = −20.5 Btu/h.
10.8 FLOW AVAILABILITY
Before we extend the availability balance to open systems, we must evaluate the availability transport associated
with mass flowing across the system boundary. Consider an incremental amount of mass dm moving with velocity
V crossing the system boundary at height Z in a time interval dt. This mass carries with it an incremental
amount of available energy, dA, defined as
ðdAÞ mass
flow
= aðdmÞ = ½u − u 0 + p 0 ðv − v 0 Þ − T 0 ðs − s 0 Þ + V 2 /2g c + gZ/g c ŠðdmÞ