First Name ___________________Last Name ____________________
CIRCLE YOUR LECTURE BELOW:
Div. 1 – 08:30 am
Prof. Chen
Div. 2 – 11:30 am
Prof. Braun
FINAL EXAM
INSTRUCTIONS
1. This is a closed book examination. You are allowed to have four single sheets of 8.5 in. x 11
in. paper with notes on both sides for the examination. All needed property tables are
provided.
2. Do not hesitate to ask the instructor if you do not understand a problem statement.
3. Start each problem on the same page as the problem statement. Write on only one side of the
page. Materials on the back side of the page will not be graded.
4. Put only one problem on a page. A second problem on the same page will not be graded.
5. If you give multiple solutions, you will receive only a partial credit although one of the
solutions is correct. Delete the solutions you do not want.
6. For your own benefit, please write clearly and legibly. Maximum credit for each problem is
indicated below.
7. After you have completed the exam, at your seat, put your papers in order. This may mean
that you have to remove the staple and re-staple. Do not turn in loose pages.
8. Once time is called you will have three minutes to turn in your exam. Points will be
subtracted for exams turned in after these three minutes.
Problem
Possible
1
40
2
30
3
30
4
30
5
30
Total
160
Score
1
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Problem 1. (40 points) This problem consists of 20 parts. Each part is 2 points. Place your brief
answers in the boxes.
a) The second law says that “all real processes are irreversible”. Does
this mean that, no matter what method one may use, air after a
compression process cannot be restored to its initial state? Yes or
No?
b) Which state has higher exergy, (a) dead state, (b) a state with a
temperature 10 K lower than the environment?
c) Is the exergy of a system different in different environments?
d) Is the following statement correct? “Since power plant A has a
higher thermal efficiency than power plant B, power plant A must
have a higher second-law efficiency than power plant B.”
e) Can the change in flow exergy for an open system be negative?
f) Is the following statement correct? “If one mole of gas A is mixed
with one mole of gas B, the mass fraction of gas A can never be
equal to that of gas B.”
g) Is the following statement correct? “With the enthalpy departure
equation, one can evaluate enthalpy change of a fluid without the
ideal gas enthalpy of the fluid.”
h) Is the following statement correct? “In ME300, we have studied a
device that can condition air along a constant relative humidity
line.”
i) For which of the following two cases is the enthalpy departure
negligible, (1) ideal gas, (2) critical point?
j) Which of the following corresponds to an ideal gas, (1) Z = 1.0, (2)
Z = 0.0, or (3) Z = pv/RT?
2
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Problem 1. (continued)
k) Methane (CH4) is burnt to form CO2, H2O, and CO. Is it complete
combustion?
l) For methane, is the air-fuel ratio expressed on a mole basis
identical to the air-fuel ratio expressed on a mass basis?
m) Which element is more likely to dissociate into its monatomic form
at 3000 K, H2 or N2?
n) Consider a mixture of CO2, CO, and O2 in equilibrium at a
specified temperature and pressure. Now the pressure is tripled.
Will the K increase, decrease, or remain the same?
o) At 2100 K, H2O ļ OH + ½ H2 has with K = 1.6749×10-4. Would
you include this reaction at 2100 K for simultaneous reactions?
p) If the compression ratio for an Otto engine is increased, will its
efficiency increase, decrease, or remain the same?
q) With the same compression ratio, which engine has higher
efficiency: Otto or Diesel?
r) An air-standard power cycle consists of two isentropic and two
constant-pressure processes, what is the name of the cycle?
s) For an open system, which compression process requires more
work input, isothermal or isentropic?
t) Which cycle has a higher thermal efficiency, (1) ideal Brayton
cycle or (2) ideal Brayton cycle with regeneration?
3
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Problem 2. (30 points) A turbine operating at steady state with steam entering at p1 = 30 bar,
T1 = 350oC and a mass flow rate of 10 kg/s. A half of the stream is extracted at p2 = 5 bar, T2 =
200oC. The remaining steam exists at p3 = 0.15 bar, x3 = 0.90. Neglect the heat loss from the
turbine to the environment at To = 25oC and po = 1 bar. Determine
(a) The total work produced by the turbine, in
kW
(b) The exergy destruction, in kW
(c) The second-law effectiveness (or exergetic
efficiency) for the turbine
p1 = 30 bar
T1 = 350oC
1 = 10 kg/s
m
Po = 1 bar
To = 25oC
Please circle your answers!
State
p
(bar)
T
( C)
h
(kJ/kg)
s
(kJ/kg·K)
1
30
350
3115.3
6.7428
2
5
200
2855.4
7.0592
3
0.15
53
2361.7
7.2831
o
p2 = 5 bar
T2 = 200oC
2 = 5 kg/s
m
p3 = 0.15 bar
x3 = 0.90
3 = 5 kg/s
m
Assumptions:
4
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5
First Name ___________________Last Name ____________________
Problem 3. (30 points) Utah Center Building uses outdoor air (state 1) at 35oC and 20%
relative humidity to cool water by direct evaporation to state 5. The relative humidity at state 5 is
100% and energy added from the water spray is negligible. Then the cooled water runs through a
cooling coil to cool the outdoor air in the air conditioning system to state 2. With a perfect
cooling coil, T2 = T5. The air is then further cooled down to 15oC at state 3 by another cooling
coil with chilled water. Finally, the air in the air conditioning system is cooled down by direct
evaporative cooling to a relative humidity of 100% at state 4 before it is sent to a room. The
moisture generated in the room is negligible and the heat generation rate in the room is 2 kW.
The room air temperature in the summer is maintained at 25oC.
(a) Label states 1, 2, 3, 4, 5, and room air
and processes 1-2-3-4-room air on the
psychrometric chart
(b) Complete the following table by using
the psychrometric chart, excluding the
shaded cells
(c) Determine the required supply airflow
rate, in kg/s
.
5
100%
35oC
20%
15oC
1
Please circle your answer for (c)!
2
3
35oC
20%
Assumptions:
(b)
State
Temperature
[oC]
Relative humidity
[%]
Humidity ratio
[kgv/kga]
Enthalpy
[kJ/kg]
1
1
2
100%
3
4
35
20
4
Room
25
100
6
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(a)
(c)
7
First Name ___________________Last Name ____________________
8
First Name ___________________Last Name ____________________
Problem 4. (30 points) Water vapor (H2O) is heated at 1 atm from 298 to 3000 K. The
chemical composition at 3000 K is found to be H2O, H2, O2, and OH. Please circle the correct
dissociation equation from the following ones and determine the corresponding value of a in the
equation you choose. You must show the calculation to receive credit.
H2O ĺ 0.568 H2O + 0.324 H2 + 0.108 O2 + a OH
H2O ĺ 0.676 H2O + 0.243 H2 + 0.081 O2 + a OH
H2O ĺ 0.784 H2O + 0.162 H2 + 0.054 O2 + a OH
9
First Name ___________________Last Name ____________________
10
First Name ___________________Last Name ____________________
Problem 5. (30 points) Air enters the compressor of an open Brayton cycle with regeneration at
100 kPa, 300K and with a mass flow rate of 2 kg/s. The compressor pressure ratio is 10, and the
inlet temperature for the turbine is 1400 K. The compressor has an efficiency of 80%. The heat
loss through the compressor is 100 kW. The entropy at the compressor outlet is the same as that
at the inlet due to the heat loss. The regenerator effectiveness is 100%. The adiabatic turbine has
an isentropic efficiency of 80%. Assume constant specific heat of Cp = 1.005 kJ/kg·K and k =
1.4. Neglect pressure drop in the piping system, regenerator, and combustor.
(a) Draw the processes on the T-s chart
and label the states
(b) Complete the following table and
also show the calculations
(c) Calculate the thermal efficiency of
the cycle
Compressor
Turbine
qC
qin
Regenerator
air
1
2
qR
x
Combustor
3
exhaust gases
T
y
4
State
P [kPa]
T [K]
1
100
300
2
x
3
s
1400
4
y
100
Assumptions:
11
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12
First Name ___________________Last Name ____________________
13