1. (36 points) Conceptual Questions (Cite all sources used in answering these questions, e.g.
lecture 21, Moran page 158, proper citation of an IEEE Journal article, Table A22, …)
(a) (5 points) A mixture of water and water vapor having a temperature T = 68◦F is heated
at constant pressure until all the water evaporates. What is the final density of the water
vapor in lb/ft3
?
(b) (5 points) A Rankine cycle has been designed for use on the space station. Should it
include a radiator or a condenser to reject heat? Explain.
(c) (6 points) Identify the law of thermodynamics (zeroth, first, second) that is most applicable to the following:
(a) Heat always flows from a hotter body to a colder body. [ 0 1 2 ]
(b) Plants convert electromagnetic radiation from the sun into chemical energy. [ 0 1 2 ]
(c) A mercury thermometer can be used to measure temperature. [ 0 1 2 ]
(d) (5 points) In an Lox/LH2 rocket engine, the reaction H2 +
1
2O2 → H2O releases massive
amounts of energy plus water vapor, which expands and exits the engine nozzles providing
the thrust for a rocket to launch. The fuel is stored as a liquid at temperature T0, and the
steam exits the combustion chamber at temperature T. In your analysis of the reactor,
you determine that the enthalpy of the steam leaving the combustion chamber/entering
the nozzle is:
h¯H2O(T) = h¯H2
(T0) + 1
2
h¯O2
(T0)
from which you can determine the exit velocity (neglecting the enthalpy of the water vapor
as it exits the nozzle because it is at much lower pressure and temperature)
V
2
2
≈ hH2O(T)
Is your analysis correct or have you missed something? Explain.
ENGR 330 Final Exam – Page 3 of 8 Due at 5 PM Nov 24, 2020
(e) (5 points) What is the efficiency of an Otto cycle with a compression ratio r = 16 using
a cold-air standard basis?
(f) (10 points) Both fuel supply and thermal pollution considerations strongly favor the development of high temperature, high efficiency power plants. One option that has been
explored by the Department of Energy uses a potassium Rankine vapor cycle that operates
at a higher temperature than the water vapor cycle. The heat rejected by the potassium
topping cycle is used as the heat source for the water vapor bottoming cycle. Assuming
that the thermal efficiency of the water cycle is ηw = 40% and the thermal efficiency of
the potassium cycle is ηK = 22%. The efficiency of the combined cycle can be shown to
be (extra credit if you show it):
η = ηK + ηw − ηKηw
Assuming the amount of fuel required is proportional to the heat input into the cycle
determine (a) what percentage of fuel is saved by adding the topping potassium vapor
cycle and (b) by what precentage is the thermal pollution reduced?
ENGR 330 Final Exam – Page 4 of 8 Due at 5 PM Nov 24, 2020
2. (24 points) Wind Generation
Iowa is a national leader in wind energy and is the first state to generate over 30% of its
electricity from wind. Wind energy also significantly benefits the economy of Iowa as manufacturing, operations and maintenance of wind farms provides at least 8000 jobs in the state,
while landowners in rural Iowa receive approximately $25 million dollars per year in land lease
payments. The figure shows the typical size of wind turbines used in farms throughout the
state. The minimum wind speed required for power generation is called the cut-in speed, which
is around 9 mph and the optimum power is achieved with a wind speed around 30 mph.
(a) (12 points) Use control volume analysis to estimate the ratio of the power generated at 9
mph and 30 mph assuming conditions having the same temperature and air pressure. For
an estimate of the power generated, you may assume that roughly the same fraction of
kinetic energy of the wind is converted into work and you should list any additional model
assumptions.
ENGR 330 Final Exam – Page 5 of 8 Due at 5 PM Nov 24, 2020
(b) (12 points) During the winter, the air temperature at night in Iowa can drop to −15◦C,
while in the summer the high temperature can be around 30◦C. Determine the ratio
of power generation on a hot summer day compared with a cold winter night assuming
that the wind speed and air pressure are the same. (It should be noted that the coldest
temperatures typically occur when there is less wind, so additional factors would need to
be included when analyzing the seasonal dependence of wind energy generation).
ENGR 330 Final Exam – Page 6 of 8 Due at 5 PM Nov 24, 2020
3. (35 points) Concentrated Solar Power (CSP) Plant
CSP is a proven means of solar power generation and new technologies are lowering its cost
curve, but a common characteristic of current CSP technologies is the use of steam turbines for
power generation. Steam turbines, although well understood, consume large amounts of water
and require extensive balance-of-plant equipment. CSP works best in regions with a lot of sun
year-round, and these tend to be desert areas where water is in short supply and permission to
use water may be difficult or impossible to obtain.
The Brayton cycle provides an attractive alternative because it only utilizes air. Consider the
following Brayton cycle. Air enters the compressor at 100 kPa and 300K and is compressed
to 1.67 MPa. As the air passes through the solar receiver device it is heated at a rate Q˙
in =
2525kW. The heated air then expands through the turbine and is exhausted. The isentropic
efficiency of the compressor is 87% and the isentropic efficiency of the turbine is 89%. The
mass flow rate through the cycle is ˙m = 5kg/s.
(a) (5 points) Describe your model assumptions
(b) (5 points) Provide an accurate sketch of the cycle on a T-s diagram and the process flow
diagram (label all states that you will use in your analysis, e.g. 1, 2s, 2, …)
ENGR 330 Final Exam – Page 7 of 8 Due at 5 PM Nov 24, 2020
(c) (20 points) Determine the electrical power output (it is not necessary to interpolate unless
the table value of a reference state is different by more than 1 percent)
(d) (5 points) Determine the overall efficiency. If the efficiency is less than the typical Rankine
efficiency of 42%, how could the cycle be improved?
ENGR 330 Final Exam – Page 8 of 8 Due at 5 PM Nov 24, 2020
4. (20 points) Hydropower Plant at Hoover Dam
Hoover Dam is 726 feet (221 metres) high and 1,244 feet (379 metres) long at the crest. Four
reinforced-concrete intake towers located above the dam divert water from the reservoir into
huge 9-m diameter steel pipes called penstocks. The water is distributed into several smaller 4-
m diameter pipes, and each pipe supplies one of the 17 vertical hydraulic turbines approximately
160 m below the dam water level. Consider a single main turbine with a volume flow rate of 80
m3/s. Estimate the maximum possible power that each turbine can deliver and the total power
capacity of the power plant. Clearly describe all model assumptions as part of your analysis.
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