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ME 200 – Thermodynamics I, Spring 2013
CIRCLE YOUR LECTURE BELOW:
Div. 5 – 7:30 am
Prof. Naik
Div. 2 – 10:30 am
Prof. Braun
Div. 4 – 12:30 am
Prof. Bae
Div. 3 – 2:30 pm
Prof. Chen
Div. 1 – 4:30 pm
Prof. Chen
Div. 6 – 4:30 pm
Prof. Hall
FINAL EXAM
INSTRUCTIONS:
This is closed book and closed notes exam. You are only allowed to use the basic
equation sheet and property tables attached here, a pen/pencil, and a simple calculator.
Show your work clearly and follow the standard problem solving procedure for problems 2
to 4. Although you may not be able to complete the calculations for some of the problems,
significant credit for problems 2 to 4 will be given if you draw control mass/volume and list all
assumptions, basic equations and methods by which you propose to solve the problem correctly.
Do not hesitate to ask the instructor if you do not understand a problem statement. For your
own benefit, please write clearly and legibly. Work only on one side of each page. If you need
extra space, work on the extra paper available, and clearly indicate problem to which the work
refers. If you give multiple solutions, you will receive only a partial credit although one of the
solutions might be correct. Delete the solution you do not want graded. Maximum credit for each
problem is indicated below.
Important Note: The use of PDAs, iPads and other tablets, cell phones, laptop computers,
or any other sources of communication (wireless or otherwise) are strictly prohibited during
examinations. Doing so is cheating. If you bring a cell phone or other communication device to
the examination, they must be turned off prior to the start of the exam, placed in your
backpack, and the backpack stored below your seat, and only picked up as you leave the
examination room for the final time. They are not to be turned on again until after you have
exited the examination room. Otherwise it will be considered a form of cheating and treated as
such.
Problem
Possible
1
50
2
50
3
50
4
50
Total
200
1
Score
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Problem 1: (50/200 points)
The standard problem solving procedure is not required for Problem 1. If required, you
should support your answers by providing appropriate arguments, equations, tables, or
charts in order to receive a full score. Place your final answer in the box provided.
(a) (5 points) Please identify which of the following parameters is not a property: temperature,
reduced temperature, pressure, relative pressure, reduced pressure, heat, and specific heat.
(b) (5 points) Does hfg increase, decrease, or remain the same when pressure increases? Explain.
(c) (5 points) A room is heated by an iron that is left plugged in. Take the entire room, including
the iron, as the system. Is this a heat or work interaction? Explain.
(d) (5 points) When two water streams are mixed in an adiabatic mixing chamber, can the
mixture temperature be lower than the temperature of both stream under a certain condition?
Explain.
(e) (5 points) In the absence of any friction and other irreversibilities, can a heat engine have an
efficiency of 100 percent on the earth? Explain.
2
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Problem 1: (Continued)
 
W
(f) (5 points) Does a cycle for which
enough information) Explain.
 0 violate the Clausius inequality? (Yes, No, or Not
(g) (5 points) From class we learned that an Otto cycle is more efficient than a Diesel cycle if
both cycles operate at the same compression ratio. Is a real diesel engine typically more efficient
or less efficient than a gasoline (Otto) engine? Explain.
(h) (5 points) A steam power plant operates on a simple, ideal Rankine cycle. Steam enters the
turbine as a saturated vapor. Now the heat input in the boiler is increased so that the steam enters
the turbine as a superheated vapor, while the boiler pressure and condenser pressure remain
unchanged. Does the net work of the cycle increase, decrease, or remain the same? Explain.
(i) (10 points) Which requires more work to compress 1 kg/s of steam by a compressor or to
compress 1 kg/s liquid water by a pump from 1 bar to 10 bar? Assume internally reversible and
adiabatic compression and neglect kinetic and potential energy effects. Explain.
3
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Problem 2: (50/200 points)
Given:
A new air-standard power cycle is proposed. Air undergoes the following four processes inside a
piston-cylinder device.
Process 1-2: Isothermal compression from P1 = 100 kPa and T1 = 300 K to P2 = 1000 kPa,
transferring 198.3 kJ/kg heat to the environment;
Process 2-3: Constant volume process during which heat is added q23 = 1000 kJ/kg;
Process 3-4: Isentropic (reversible and adiabatic) expansion to P4 = 100 kPa;
Process 4-1: Constant pressure process during which heat is rejected.
Neglect kinetic and potential energy effects. Assume constant specific heats for air.
Rair = 0.287 kJ/kg˖K, cv = 0.718 kJ/kg˖K, cp = 1.005 kJ/kg˖K, k = 1.4
Find:
(a) Draw the processes of the cycle in the T-s diagram on the next page. Clearly label the states
and mark the direction of the process. Do not show any property values on the diagram. The P-v
diagram for the cycle is shown on the next page as an example;
(b) Complete Table P-1 on the next page (If calculations are need, please show them to receive
credits.);
(c) Calculate thermal efficiency (%) of the cycle.
System sketch: Please show the control mass used.
Assumptions:
Basic equations:
4
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Solution:
(a)
T
P
3
2
4
1
v
s
(b)
Table P-1
State
Pressure
(kPa)
Temperature
(K)
Specific volume
(m3/kg)
Specific internal energy
(kJ/kg)
1
100
300
0.861
215.4
2
1000
300
0.0861
215.4
3
4
100
(c)
5
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6
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Problem 3: (50/200 points)
Given:
A vapor compression refrigeration cycle uses steam as the working fluid. The evaporator absorbs
heat at 35°F. The saturated steam at state 1 has a mass flow rate of 1.0 lb/s and passes a poorly
insulated compressor. The steam pressure is increased to 5 psia after the compression. The heat
transfer from the compressor to the surrounding is 100 Btu/s so that h2 = h2s. The boundary and
surrounding temperature of the compressor is measured to be 540°R. Then the steam rejects
heats to the surrounding by the condenser and then passes through the throttling device and
evaporator to complete the cycle. Assume there are no pressure drop in condenser and
evaporator. Neglect kinetic and potential energy changes. Do not interpolate but use the closest
table values.
Find:
(a) Draw the processes for the cycle on the T-s chart on the next page. Clearly label the states
and mark the direction of the processes. Do not show any property values on the chart;
(b) Complete Table P-2 on the next page (If calculations are need, please show them to
receive credits.);
(c) Calculate the work input to the compressor; in Btu/s;
(d) Determine the isentropic efficiency of the compressor;
(e) Calculate the COP of the refrigerator;
(f) Calculate the entropy generation of the compressor, in Btu/s˖oR.
System sketch: Please show the control volume used for the compressor.
P2=5 psia
x3=0
Condenser
Tcv=540 °R
Evaporator
T1=35°F
x1=1
4
Assumptions:
Basic equations:
8
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Solution:
(a)
T
s
(b)
Table P-2
State
P
(psia)
T
(°F)
1
0.0999
35
2 & 2s
5
3
5
162.21
4
0.0999
35
h
(Btu/lb)
s
(Btu/lb-°R)
x or phase
1
SHV
130.17
(c)
9
0.2349
0
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Problem 4: (50/200 points)
Given:
An inventor has developed a “two-phase compressor” that consists of an adiabatic phase
separation tank, an adiabatic and reversible pump, an adiabatic and reversible compressor,
and an adiabatic mixing chamber, as shown in the schematic diagram below. The inventor
claims that the use of the two-phase compressor enables an isothermal heat addition and
therefore is closer to a Carnot cycle. A two-phase water-steam mixture with a flow rate of 25
kg/s enters the compressor at a pressure of 0.8 bar at state 1. Liquid is separated from the vapor
in the adiabatic phase separation tank. The liquid is compressed in the reversible adiabatic pump
while the vapor is compressed in the reversible adiabatic compressor. Both flows are mixed in
the adiabatic mixing chamber to produce the saturated liquid with a pressure of 6 MPa (state 2)
at the exit. Neglect the kinetic and potential energy effects. Assume the water liquid is
incompressible. Do not interpolate but use the closest table values. Note that m 1b  x1  m 1 .
Find:
(a) Depict properly all of the state points (1, 1a, 1b, 2a, 2b, and 2) on the T-s diagram on the
next page and show lines of constant pressure of P1 and P2;
(b) Complete Table P-3 in the following page (If calculations are need, please show them to
receive credits.);
(c) Determine the specific work input requirement for the pump, in kJ/kg;
(d) Determine the overall entropy generation for the two-phase compressor, in kW/K;
(e) Identify which the following components has irresibilities in the two-phase compressor:
(1) 2-phase separator, (2) pump, (3) compressor, (4) mixing chamber, (5) none of these.
System sketch: Please show the control volume you used for part (d).
Assumptions:
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Basic equations:
Solution:
(a)
T
s
(b)
Table P-3
State
P
h
s
x/Phase
(MPa)
(kJ/kg)
(kJ/kg˖K)
(-)
1
0.08
1a
0.08
391.66
1.2329
0
1b
0.08
2665.8
7.4346
1
2a
6
2b
6
2
6
0
(c)
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