AME 230-Midterm Exam 1-Fall 2023-Answers
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1
Fall 2023
AME 230 -Thermodynamics
Midterm Exam # 1 Answers
September 18, 2023
•
You will have about
50 Minutes
for this exam.
•
This is a closed-note and closed-book exam.
•
Useful formulas, constants and tables are provided.
•
Answers to problems
8 and 9
should use Use thermodynamics problem-solving
method.
•
Neatness is very important. If I cannot follow the solution, that problem will
not be graded.
I, ______________________________ (Print Name), with ID #___________________,
Understand that I should NOT receive any unauthorized help from or give any unauthorized help
to anyone else during this exam; otherwise, I will get an automatic “F” in this exam.
< signature >____________________
Score
2
Midterm #1, AME 230, Fall 2023
Print Name (clearly)
1. Indicate whether the following statements are true or false (each 3 point)
a) The specific volume is not the reciprocal of the density.
A: True
B: False
b) Work is energy transfer for which the sole effect on everything external to the system
could have been the raising of a weight.
A: True
B: False
c) A system may contain energy in the form of heat.
A: True
B: False
d) A change in the total energy of a system is described by the change in its internal, kinetic
and potential energy.
A: True
B: False
e) The temperature of a system can be changed by a heat transfer only.
A: True
B: False
f) If a closed system undergoes a thermodynamic cycle, there can be no net work or heat
transfer.
A: True
B: False
g) Water in a glass with ice cubes consists of several phases.
A: True
B: False
h) The work done by a system is taken as negative (
W
< 0).
A: True
B: False
i) Heat transfer from a system is taken as positive (Q > 0).
A: True
B: False
j) Specific heat is the energy required to raise the temperature of the unit mass of a
substance by one degree keeping volume or pressure constant
A: True
B: False
3
Midterm #1, AME 230, Fall 2023
Print Name (clearly)
2. Through a Venturi meter shown in picture below a steady flow of kerosene is established.
As the kerosene flows from point a to point b does the pressure increase or decrease as the
pipe diameter decreases? (4 point)
Answer (one word, no explanation needed):
decreases
3. What is The First Law of Thermodynamics (definition in your own words if
understandable and the standard definition are both acceptable). (4 point)
Answer:
(a)
energy is conserved
or
(a)
energy can be neither created nor destroyed during a process; it can only change
forms
4. For any particular application, energy transfer by heat can occur by one or more of three
modes. List the three modes of energy transfer by heat and name the laws associated with
each. (6 point)
Answer:
a.
Conduction (Fourier’s law)
b.
Convection (Newton’s law of cooling)
c.
Radiation (Stefan-Boltzmann law)
5. What is the quality of the liquid-vapor mixture of H
2
O if its specific volume,
υ
= 1 m³/kg
at 100°C, with
v
f
= 1.0435 × 10
-3
m³/kg and
v
g
= 1.673 m³/kg. (You do not need to Use
thermodynamics problem-solving method, but you need to clearly show all relevant
equations and calculations). (6 point)
Since
v
= (1 –
x
)
v
f
+
x
v
g
࠵? =
࠵? − ࠵?
!
࠵?
"
− ࠵?
!
=
1
࠵?
#
࠵?࠵?
− 1.0425 ×10
$#
࠵?
#
࠵?࠵?
1.673
࠵?
#
࠵?࠵?
− 1.0425 ×10
$#
࠵?
#
࠵?࠵?
= 0.597
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4
Midterm #1, AME 230, Fall 2023
Print Name (clearly)
6. A
thermodynamic cycle
is a sequence of processes that begins and ends at the same state.
List three main thermodynamic cycles and provide their sketch, clearly indicating work and
heat directions. (9 point)
Answer:
a.
Power cycle
b.
Refrigeration cycle
c.
Heat pump cycle
7. Sketch
p-T
and
T-
υ diagram based on
p-
υ-
T
surface of H
2
O. Indicate, liquid (L), vapor
(V), solid (S) and liquid-vapor (L-V) phases, where applicable. On
p-T
diagram indicate
the triple and critical point and on
T-
υ diagram indicate the critical point. (8 point)
5
Midterm #1, AME 230, Fall 2023
Print Name (clearly)
8. A residential heat pump is used to provide heating during the winter months. The heat
pump absorbs
Q
in
=1500 Btu from the outside air and requires a work input of
W
cycle
=400
Btu to operate. Determine the coefficient of performance for the heat pump cycle. Use
the diagram you draw for heat pump cycle in question 6 and clearly mark the direction of
heat and work.
Use thermodynamics problem-solving method. (13 point)
KNOWN
: The heat input and net work input for a
heat pump cycle are specified.
FIND
: Determine the coefficient of performance.
SCHEMATIC AND GIVEN DATA
:
Q
in
= 1500 Btu
W
cycle
= 400 Btu
ENGINEERING MODEL
:
1. The cycle is a heat pump cycle.
2. Energy transfers are positive in the directions of
the arrows on the figure.
ANALYSIS
:
For the heat pump cycle,
࠵? =
%
!"#
&
$%$&’
To get
Q
out
we note that Δ
E
cycle
= 0 , so
W
cycle
=
Q
out
–
Q
in
→
Q
out
=
Q
in
+
W
cycle
= 1500 + 400 = 1900 Btu
Now, the coefficient of performance (COP) for the heat pump is:
࠵? =
࠵?
’()
࠵?
*+*,-
=
1900 ࠵?࠵?࠵?
400 ࠵?࠵?࠵?
= 4.75
6
9. A total of 0.9 kg of superheated water vapor is in a piston-cylinder assembly, initially at
7 bar and 500
0
C. The water undergoes first a constant pressure process followed by a
constant volume process. At the end of the constant volume process, the water is a two-
phase liquid-vapor mixture with a quality of 0.6 and at the temperature of 150
0
C.
Determine the final pressure, the work and heat transfer for each process, all in kJ and
sketch
T
-
v
and
p
-
v
diagrams showing the key states and the processes.
Use
thermodynamics problem-solving method. (20 point)
Midterm #1, AME 230, Fall 2023
Print Name (clearly)
SOLUTION
KNOWN
: Water contained in a piston cylinder assembly undergoes two processes in series.
FIND
: Sketch the
T
-
v
and
p
-
v
diagrams and for each process determine
Q,
W
and and final pressure.
SCHEMATIC AND GIVEN DATA
:
Initial state:
p
= 7 bar,
T
= 500
0
C.
Final state:
x
= 0.6,
T
= 150
0
C.
ENGINEERING MODEL
:
1. The water is a closed system.
2. Volume change is the only work mode.
3. Process 1-2 occurs at constant pressure and Process 2-3 occurs at constant volume.
4. Kinetic and potential energy effects can be neglected.
ANALYSIS
:
First, we fix each state.
State 1 is in the superheated vapor region. From Table A-4 at 7 bar and 500
o
C:
υ
1
= 0.5070
m
3
/kg and
u
1
= 3126.8 kJ/kg.
State 3 is in liquid-vapor region at
T
3
= 150
o
C and
x
3
= 0.6. From Table 2 we can calculate
specific volume and internal energy
υ
3
=
υ
f3
+
x
3
(
υ
g3
̶
υ
f3
) = 0.0010905(m
3
/kg) + 0.6(0.3928 ̶ 0.0010905)(m
3
/kg) = 0.2361 m
3
/kg
and
u
3
=
u
f3
+
x
3
(
u
g3
̶
u
f3
) = 631.68(kJ/kg) + 0.6(2559.5 ̶ 631.68)(kJ/kg)
=
1788.4 kJ/kg.
For state 2
υ
3
=
υ
2
= 0.2361 m
3
/kg, and from Table A-3 we see that
υ
2
<
υ
g
(7 bar). Thus, the
quality at state 2 is
x
2
= (
υ
2
̶
υ
f2
)/(
υ
g2
̶
υ
f2
) = (0.2361 ̶ 0.0011080)/(0.2729 ̶ 0.0011080) = 0.8646
and
u
2
=
u
f2
+
x
2
(
u
g2
̶
u
f2
) = 696.44(kJ/kg) + 0.8646(2572.5 ̶ 696.44)(kJ/kg)
= 2279.6 kJ/kg.
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7
(
)(
)(
)
2
3
5
2
12
1
2
1
3
1
m
10 N/m
1kJ
(
)
0.9kg
7bar
0.2361
0.5070
170.7 kJ
kg
1bar
10 N m
W
pdV
mp v
v
=
=
-
=
-
=
-
×
ò
Midterm #1, AME 230, Fall 2023
Print Name (clearly)
(
)(
)
(
)
12
2
1
12
kJ
(
)
0.9kg
2279.6
3126.8
170kJ
932.48 kJ
kg
Q
m u
u
W
=
-
+
=
-
+
-
=
-
(
)(
)
23
3
2
12
kJ
(
)
0.9kg
1788.4
2279.6
442.1 kJ
kg
Q
m u
u
W
=
-
+
=
-
=
-
An energy balance reduces to give
Now, for process 2-3, the volume is constant, thus W23 = 0. The energy balance reduces to give
The final pressure from Table 2 is
4.758
bar.
Now, we can calculate work from state 1 to 2:
8
Key equations
9
Conversion factors
Constants
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