ME 322 – Mechanical Engineering Thermodynamics
Exam 3
Fall 2015
This is a non-collaborative take-home exam.
Submit your own work.
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EXAM INSTRUCTIONS – PLEASE READ THIS CAREFULLY
You will have several days to complete this exam. You may use your notes, the online
course resources, your computer (EES, Google, etc.) and pretty much any non-human
resource you can find. You are not allowed to collaborate with other students/engineers
on the exam. However, if you have a strong need to collaborate with others on this exam,
you may discuss the exam at great lengths with anyone currently pursuing a humanities
degree at the UI.
There will not be partial credit for the questions on this exam. Either you get the answer
(within reasonable error), or you don’t.
For multiple choice questions, circle the correct answer(s). Do provide details about
where your answer came from. A correct circled answer without supporting calculations
will still be given zero points.
This is a 100 point exam
Part 1: Engineering Calculations – each numbered problem is worth 10 points
Write your answers in the space below
Attach your EES code and output to the back of the exam
Problems 1-3 apply to the following description and diagram. A steam power cycle that incorporates one reheat
leg is shown in the sketch below. Steam from the boiler enters the high pressure turbine at 1850 psia, 1400°F. The
steam leaves the high pressure turbine at P[2] and then enters the reheat section of the boiler where it is reheated
back to 1200°F with no pressure drop. The steam then enters the low pressure turbine where it expands to 10 psia.
Enough heat exchange area is provided in the condenser such that the water leaving the condenser is saturated liquid
at 10 psia. Both the high and low pressure turbines have an isentropic efficiency of 85% and the pump has an
isentropic efficiency of 95%. The net power output of the cycle is 400,000 hp.
1) To maximize thermal efficiency of the cycle, at what P[2] (in psia) should the steam be taken back to the
boiler for reheat? (Hint: Conduct a parametric study to figure out the optimal value of P[2]).
2) At the optimal value for P[2], what is the value of Q_dot_in (in Btu/hr)? Remember, this should include
both the initial heating, and the reheat loop.
3) Assuming you have a high temperature reservoir at 1800 °F, and a cold temperature reservoir at 200 °F,
calculate the maximum theoretical efficiency (think Carnot) of this system?
4) A particular steam turbine can handle a maximum of 1500°F at the inlet. The exhaust pressure is 12 psia.
Under ideal (isentropic) conditions, the maximum allowable liquid in the turbine is 10%. Use EES to
calculate:
a. Under real conditions, when the turbine is not isentropic, find the maximum isentropic efficiency
(in %) that would still ensure that no liquid water was in the turbine.
b. Comment on the likelihood of there ever being liquid water in the actual turbine.
5) 5 lbm/second of saturated mercury vapor flows in to a valve. The mercury enters at 400 psia, and leaves at
10 psia. Find the following:
a. The quality of the mercury exiting the valve
b. The entropy production rate, assuming valve is adiabatic (in Btu/sec-F)
6) Using the same input as the problem above, if you were to replace the valve with an ideal turbine
(isentropic), and have the mercury exit with a quality of 0, calculate the following:
a. How much heat will be transferred out of the turbine (Btu/sec)?
b. How much power power could be generated by the turbine (Btu/sec)?
7) A house is using a heat pump with an earth-coupled isothermal source as an energy source. The heat pump
uses R134a as the working fluid. At the depth of the heat source the earth’s temperature can be assumed to
be constant year-round. This results in a year-round standard evaporating temperature of 55°F. Thermal
energy from the condenser is available at 75 F. The compressor has an isentropic efficiency of 80%.
Assume pressure drops through plumbing are negligible. The refrigerant leaves the condenser with 8
degrees of subcooling and it enters the compressor with 15 degrees of superheat. Under these conditions,
the heat pump delivers 65,000 Btu/hr to the house. Calculate the following:
a. The power requirement (hp) of the compressor
b. The mass flow of R134a (lbm/hr)
c. Coefficient of performance for heating
8) In lecture 32 we did an example calculating the work required
in a compressor for a mixture of methane and ethane. Repeat
this problem, but instead of the methane/ethane mixture, use
air. In particular, use the composition of air as given in the
beginning of Example 12.2 in your textbook. Your EES code
should be set up to be as adaptable as possible (for other
mixture compositions), and will probably have lines like:
f$[1..4] = ['N2', 'O2', 'Ar', 'CO2']
y[1] = .7809
y[2] = .2095
y[3] = .0093
y[4] = .0003
y_total = SUM(y[k], k=1, 4)
Given: A compressor is being used to move a mixture of air.
The mixture enters the compressor at 20 psia, 70°F and
leaves the compressor at 80 psia. The compressor is being
modeled as isentropic.
P2  80 psia
wc
1
P1  20 psia
T1  70F
Calculate the following:
a. Work required (Btu/lbm) to the compressor using air composition from Example 12.2
b. Work required (Btu/lbm) to the compressor using ‘air_ha’ as your fluid in EES
Part 2: Short Calculations – each problem worth 5 points
9) You have a 100 W halogen light bulb, and a 100 W LED light bulb. Assume that both produce the same
quantity of light. Under steady-state conditions, the halogen bulb operates at 1000 °C, and the LED bulb
operates at 30°C. Calculate the steady-state entropy production of each. Comment on which one you would
choose, and why.
10) What is the mass fraction of oxygen in a mixture that has equal volumes of oxygen (O2) and carbon
dioxide (CO2)?
Part 3: Multiple Choice – each problem worth 2.5 points
Some problems may have multiple answers
Problems 11-14 apply to a vapor compression refrigeration cycle that utilizes ammonia as the refrigerant.
The saturated evaporating temperature is -10 F and the saturated condensing temperature is 95 F. Saturated vapor
exits the evaporator and saturated liquid exits the condenser with no subcooling. The mass flow rate of the
refrigerant in the cycle is 300 lbm/hr.
11) What is the enthalpy of the fluid entering the evaporator?
a) 32.1 Btu/lbm
b) 149.4 Btu/lbm
c) 608.5 Btu/lbm
d) 632.6 Btu/lbm
12) What is the enthalpy of fluid exiting the evaporator?
a) 32.1 Btu/lbm
b) 149.4 Btu/lbm
c) 608.5 Btu/lbm
d) 632.6 Btu/lbm
13) What is the refrigeration capacity of this system (in tons)?
a) 5.5 tons
b) 7.5 tons
c) 9.5 tons
d) 11.5 tons
14) What is the DSC for this cycle?
a) -10 F
b) 0 F
c) 10 F
d) 95 F
Feel free to draw a picture of the cycle down below. A P-h diagram could be useful.