Modern Engineering Thermodynamics

8.3 Systems Undergoing Irreversible Processes 261
EXAMPLE 8.8 A CONTINUATION OF EXAMPLE 5.4, WITH
THE ADDITION SHOWN IN ITALIC TYPE
A food blender has a cutting-mixing blade driven by a 0.250 hp electric motor. The machine is initially filled with 1.00 qt of
water at 60.0°F, 14.7 psia. It is turned on at full speed for 10.0 min. Assuming the entire machine is insulated and the mixing
takes place at constant pressure, determine the temperature of the water and the amount of entropy produced when the
machine is turned off.
Solution
First, draw a sketch of the system (Figure 8.8).
The unknowns here are T 2 and l (S P ) 2 . The system is the water in the
blender, which we assume to be an incompressible material. The
data for the water are as follows:
State 1
p 1 = 14:7psia
T 1 = 60:0°F
Isobaric
ƒƒ!
mixing
State 2
p 2 = p 1 = 14:7psia
The solution to the first part of this problem is given in Example 5.4
as m = 2.08 lbm and T 2 =111°F.
The solution to the second part is determined by the indirect method.
Equation (8.1) gives
Z
dQ
1ðS P Þ 2 = ms ð 2 − s 1 Þ−
T b
Σ
1.00 quart of water
System boundary
1 (S P ) 2 = ?
0.250 hp electric motor
and, for an incompressible substance,
so that
s 2 − s 1 = c ln T 2
T 1
0 ðinsulated systemÞ
FIGURE 8.8
Example 8.8.
or
1ðS P Þ 2 = mc ln T 2
T 1
1ðS P
Þ 2 = ð2:08 lbmÞ½1:0 Btu/ ðlbm⋅RÞŠln = 0:195 Btu/R
111 + 459:67
60:0 + 459:67
If we wished to know the entropy production rate for this example, our analysis and results would be the same
as that for part b of Example 8.6. The entropy production rate would not be constant in time, but would
decrease as the water became hotter. Since it is stated that the blender is insulated, eventually enough mixing
energy would be converted into internal (thermal) energy to cause the water to completely vaporize, whereupon
the assumption of an incompressible fluid no longer applies.
EXAMPLE 8.9 A CONTINUATION OF EXAMPLE 5.5, WITH
THE ADDITION SHOWN IN ITALIC TYPE
A new radiation heat transfer sensor consists of a small, closed, rigid, insulated 0.0400 m 3 box containing a 0.0100 m 3
rubber balloon. Initially, the box is evacuated but the balloon contains argon (an ideal gas) at 20.0°C and 0.0100 MPa.
When the balloon receives 0.100 kJ of radiation energy through an uninsulated window in the box, it bursts. The resulting
pressure change is sensed by a pressure transducer and an alarm is sounded. Determine the pressure and temperature inside
the box after the balloon bursts and the entropy produced during this process if the average surface temperature of the heat transfer
window is 400.K.
Solution
First, draw a sketch of the system (Figure 8.9).
(Continued )