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ME 200 Homework #07 - Spring 2015
Homework Due: Wednesday, March 11, 2015
HW07(1)
In a dairy plant, milk at 40 oF is pasteurized
continuously at 160 oF at a rate of 0.4 ft3/s for 24
hours a day and 365 days a year. The milk is
heated to the pasteurizing temperature by hot
water heated in a natural gas fired boiler that has
an efficiency of 82%. The pasteurized milk is
then cooled by cold water at 65 oF before it is
finally refrigerated back to 40 oF. To save energy
and money, the plant installs a regenerator that
has an effectiveness of 82%. If the cost of natural
gas is $0.52/therm (1 therm = 100000 Btu),
determine how much energy and money the
regenerator will save this company per year. In
your analysis, you can approximate the properties
of milk as water. (Answer: $488845)
HW07(2)
For the desuperheater shown in the figure, liquid
water at state 1 is injected into a stream of
superheated vapor entering at state 2. As a result,
a saturated vapor exits at state 3. Data for steady
state operation are shown in the figure. Ignoring
stray heat transfer and kinetic energy and
potential energy effects, determine the mass
flow rate of the incoming superheated vapor, in
lbm/min. (Answer: 238.7 lbm/min)
HW07(3)
Ammonia enters the expansion valve of a refrigeration system at a pressure of 150 psia and a
temperature of 100 oF and exits at 16 psia. If the ammonia undergoes a throttling process, what is
the quality of the ammonia exiting the expansion valve? (Answer: 0.188)
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HW07(4)
Air flows through a system shown below. The pressure and temperatures for air at specific
locations within the system have been measured and indicated. The compressor requires 10,000
kW for its operation at steady state. Between the compressor exit and turbine inlet, air is cooled
using water flowing at 3000 kg/min. The water enters at 25C and leaves at 40C at 1 atm.
Specific heats of air are not constant.
Compressor
Win = 10,000 kW
Turbine
P4 = 1 bar
T4 = 800 K
P2 = 20 bars
T2 = 1400 K
P1 = 5 bars
T1 = 1100 K
P3 = 18 bars
T3
Heat
Exchanger
Water Out
P6 = 1 bar
T6 = 40C
Water In
P5 = 1 bar
T5 = 25C
(a) Complete the table below.
State
P
(kPa)
T
(°C)
v
3
(m /kg)
h
(kJ/kg)
1
2
3
4
(b) Determine the mass flow rate (kg/s) of air through the system. (Answer: 28.2 kg/s)
(c) Compute the power developed by the turbine (MW). (Answer: 16.4 MW)
HW07(5)
Saturated liquid refrigerant 134a enters a throttling valve at 8 bar. The pressure of refrigerant at
the exit of the throttling device is 1.8 bar. The refrigerant then enters a heat exchanger in which
it is heated to saturated vapor at 1.8 bar. The volumetric flow rate at the exit of the heat
exchanger is 500 L/min. The refrigerant leaving the heat exchanger is adiabatically compressed
to 7 bar and 50C.
(a) What is the temperature (C) at the exit of the throttling valve?
(b) Calculate the rate of heat transfer (kJ/min) in the heat exchanger.
(c) How much power (kW) is required to run the compressor? (Answer: -3.54kW)
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HW07(6)
As shown in the figure, hot industrial
waste water at 200 psia, 400 oF with a
mass flow rate of 10 lbm/s enters a
flash chamber via a valve. Saturated
vapor and saturated liquid streams,
each at 60 psia, exit the flash chamber.
The saturated vapor enters the turbine
and expands to 1 psi, x = 90%. Stray
heat transfer and kinetic and potential
energy effects are negligible. For
operation at steady state, determine
the power, in hp, developed by the
turbine. (Answer: 30.53 hp)
HW07(7)
(a) Is it possible for a heat engine to operate without rejecting any waste heat to a lowtemperature reservoir? Explain.
(b) In the absence of any friction and other irreversibilities, can a heat engine have an
efficiency of 100%?
(c) Are the efficiencies of all the work-producing devices, including the hydroelectric power
plants, limited by the Kelvin-Planck statement of the second law? Explain.
HW07(8)
Shown in the figure is a proposed system that
undergoes a cycle while operating between cold
and hot reservoirs. The system receives 500 kJ
from the cold reservoir and discharges 400kJ to
the hot reservoir while delivering net work to its
surrounding in the amount of 100kJ. There are
no other energy transfers between the system
and its surroundings. Evaluating the
performance of the system using:
(a) Clausius statement of second law;
(b) The Kelvin-Planck statement of second law.
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