me321:winter 2008 endterm test ---------------
name_______________________________
* Closed notes, open book test. You may use a single handwritten
8.5 x 11" help sheet.
* Answer any four of the six questions. Each question is worth
50 points. Please indicate clearly which questions you do not
wish to have graded by drawing a line through the respective
question statement.
[The various numerical answers
to the problems below are shown in red]
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Questions 1, 2, 3 and 4 relate to the geothermal steam power plant
shown below, which is proposed to provide enery to a community
of 300 households. It uses an underground geothermal energy source
to boil the compressed liquid water to a temperature of 200°C
at the inlet of the turbine.
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1. Consider the steam power plant shown above
operating under the conditions shown in the diagram. Assume that
the pump power is negligible, Using values obtained from the tables,
determine
a) The power output of the adiabatic turbine (kW) [314.5kW]
b) The thermal efficiency of the power plant (hth) [10.7%]
c) Draw the complete cycle on the P-h diagram provided
below, clearly showing the four
processes (1) - (2) - (3) - (4) - (1).
Justify all values
used and derive all equations used starting from the basic
energy equation for a flow system and the basic definition of
thermal efficiency of a heat engine.
Note: liquid water has a density of 1 kg/liter.
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P-h diagram for
water - associated with Question 1:
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2. Consider the adiabatic turbine only in the
power plant shown above. Using values obtained from the tables,
determine
a) The actual specific work done by the turbine (kJ/kg) [285.9 kJ/kg]
b) The isentropic specific work done by the turbine (kJ/kg) [491.7 kJ/kg]
c) The turbine adiabatic efficiency (hT) [58%]
d) Draw both the actual and the isentropic turbine processes on
the h-s diagram provided below. On this diagram indicate
the relevant specific work done for each of these processes.
Justify all values
used and derive all equations used starting from the basic
energy equation for a flow system and the definition of turbine
adiabatic efficiency.
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h-s diagram for
steam - associated with Question 2:
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3. Consider the steam power plant shown above.
We wish to evaluate the theoretical maximum possible thermal efficiency
(hth)
that can be attained by the power plant operating under the conditions
shown.
a) Choose the high and low temperatures for this evaluation, and
explain and justify your choice. [TH = 200°C (473K), TL = 20°C (293K) alt. TL
= 45.8°C (318.8K)]
b) Derive the equation for the maximum thermal efficiency starting
with the basic definition of thermal efficiency of a heat engine.
c) Evaluate the maximum possible thermal efficiency, and state
at least two reasons why the actual power plant shown above cannot
attain this maximum. [38.1%
(32.6%)]
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4. Consider the feedwater pump of the geothermal
plant shown above operating under the conditions shown in the
diagram. Assume that the pump is adiabaic, the inlet and outlet
pipe diameters are the same and that the temperature of the water
increases by 0.1°C due to friction as it passes through the
pump. Determine
a) the input power required to drive the pump under the conditions
shown [W]. [669W]
b) the power required to drive an equivalent
isentropic pump [W]. [209W]
c) the pump efficiency (hP) defined as the isentropic pump work divided by the
actual pump work required to drive the pump. [hP = 31.3%]
Justify all values
used and derive all equations used starting with the basic
steady flow energy equation, and the enthalpy change and isentropic
relation for incompressible liquids.
Note: liquid water has a density of 1 kg/liter and a specific
heat capacity of 4.18 kJ/kg K.
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5. The expansion stroke of an ideal Stirling
cycle refrigerator can be represented by a piston-cyclinder device
which expands at a constant temperature. Consider a piston-cylinder
device containing helium gas which absorbs heat at a constant
temperature of -20°C while expanding from an initial pressure
of 2MPa and initial volume of 30 cubic centimeters to a final
volume of 35 cubic cm.
a) Sketch the process on a P-v diagram clearly indicating
the initial and final states with respect to the relevant constant
temperature lines. On the diagram indicate the work done during
this process.
b) Determine the work done and the amount of heat absorbed
during this process [Joules]
[Qabsorbed = W = 9.25Joules/stroke]
Derive all equations
used starting with the basic energy equation for a non-flow system,
the definition of boundary work done, the ideal gas equation of
state and the equation of internal energy change of an ideal gas.
Note that under the above conditions helium can be treated as
an ideal gas.
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6. Two components of a refrigeration system are shown below.
a) On the P-h diagram provided below
draw the processes as the refrigerant passes through the two components
above, clearly showing the stations (1)-(2)-(3) on the diagram.
b) Assuming that the throttle is adiabatic, use the R-134a tables
to determine the heat transferred to the evaporator (kJ/kg), and
the temperature of the refrigerant leaving the evaporator (T3).
[qevap = 142.4kJ/kg, T3
= -22.36°C]
Justify all values
used and derive all equations used starting with the basic
energy equation for a flow system.
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P-h diagram for R134a - associated with Question 6
