Modern Engineering Thermodynamics

262 CHAPTER 8: Second Law Closed System Applications
EXAMPLE 8.9 (Continued )
Window
T window = 400. K
Rigid insulated box
with a volume of
0.0400 m 3
Argon-filled balloon
initially with a volume
of 0.0100 m 3 at 20.0°C
and 10.0 kPa
FIGURE 8.9
Example 8.9.
The unknown is the entropy produced during this process if the average surface temperature of the heat transfer window is
400. K. The material is argon gas.
In Example 5.5, we use an energy balance to find the final pressure and temperature as p 2 = 4.15 kPa and T 2 = 214°C = 487 K.
Now, an entropy balance gives
1Q 2
T b
which can be solved for the entropy production as
+ 1 ðS P Þ 2
= mðs 2 − s 1 Þ argon
1ðS P Þ 2 = mðs s − s 1 Þ − 1 Q 2
T b
and, since argon is an ideal gas, we can write
s 2 − s 1 = c p ln ðT 2 /T 1 Þ− R ln ðp 2 /p 1 Þ
From Table C.13b of Thermodynamic Tables to accompany Modern Engineering Thermodynamics, we find that for argon,
c p = 0.523 kJ/kg · KandR =0.208kJ/kg· K; and from Example 5.5, the mass of the argon is m = 0.00164 kg. Then, with
1Q 2 =0.100kJandT b = 400. K, we get
214 + 273:15 K
4:15 kPa
1ðS P Þ 2 = ð0:00164 kgÞ ð0:523 kJ/kg.KÞ ln
− ð0:208 kJ/kg.KÞln
20:0 + 273:15 K
10:0kPa
0:100 kJ
−
400: K = 0:486 × 10−3 kJ/K = 0:486 J/K
In this example, the heat transfer occurs over only a portion of the system’s surface (the uninsulated window). The rest of
the enclosure is insulated to prevent the sensor from being influenced by anything except the heat source in front of the
window. Though the surface temperature of the window probably changes during the heat transfer process, an adequate
solution is obtained simply by using an average surface temperature during the process of T b = 400. K.
Exercises
14. Suppose the balloon in Example 8.9 is designed to burst after absorbing 0.200 kJ of radiation heat transfer. Determine
the entropy produced during this process if the average surface temperature of the heat transfer window is 500. K.
Answer: 1 (S P ) 2 = 0.336 J/K.
15. If air were substituted for the argon in Example 8.9 with no changes in the remaining parameters, what would be the
entropy produced inside the box during this process? Answer: 1 (S P ) 2 = 0.510 J/K.
16. Determine the entropy produced when the radiation heat transfer is increased to produce a final pressure of 20 kPa in
the box after the balloon bursts. Assume that the average temperature of the heat transfer window is 1200 K for this
process. Answers: 1 (S P ) 2 = 0.664 J/K.
EXAMPLE 8.10 A CONTINUATION OF EXAMPLE 5.6, WITH
THE ADDITION SHOWN IN ITALIC TYPE
Suppose 0.100 lbm of Refrigerant-134a initially at 180.°F and 100. psia in a cylinder with a movable piston undergoes the
following two-part process. First, the refrigerant is expanded adiabatically to 30.0 psia and 120.°F, then it is isobarically compressed
to half its initial volume. Determine
a. The work transport of energy during the adiabatic expansion.
b. The heat transport of energy during the isobaric compression.