me321:fall 2007 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 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 proposed vapor-compression
home heat pump system using refrigerant R134a, as shown below.
Notice that the evaporator is placed outside, thus heat is pumped
from the surroundings at -5°C in order to raise the temperature
of the air and maintain the inside home temperature at a comfortable
25°C..
1. Sketch the complete heat pump cycle above on the P-h
diagram provided, showing clearly all four processes (1) - (2)
- (3) - (4) - (1). Using the conditions shown on the diagram above
and values obtained from the tables, evaluate the heat transferred
from the condenser to the air in the heating duct [2.76
kW], and the actual Coefficient of Performance (COPHP) of the heat pump system, neglecting the
work done by the fan [COPHP = 3.45].
Justify all values used and derive all equations
used starting from the basic steady flow energy equation and the
basic definition of COPHP.
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2. Consider the case that the air temperature inside the home
is 10°C. Using the conditions shown on the diagram above,
evaluate the heat transferred from the condenser to the air in
the heating duct [2.76 kW]. Assuming
that there is no heat loss to the outside air and neglecting the
work done by the fan, determine time required to heat the 500
cubic meters of air in the home to 25°C [~39
minutes].
Justify all values used and derive all equations
used starting from the basic steady flow energy equation, the
basic non-flow energy equation, the ideal gas equation of stete
and of internal energy change.
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3. Consider the compressor only in the diagram above. Using the
conditions shown on the diagram together with values obtained
from the steam tables, carefully draw the compression process
(1) (2) on the h-s diagram provided below. Show also
the equivalent isentropic process on the sketch and determine
the compressor adiabatic efficiency [hC = 73.7%].
Is this a feasible compressor design? Determine the total entropy
generated associated with the compression process (compressor
and surroundings) to justify your conclusions [sgen =
0.0446 kJ/kg.K > 0: feasible].
Justify all values used and derive all equations
used starting from the basic steady flow energy equation and total
entropy change (system and surroundings) for a flow system.
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4. Consider the problem of a heat pump which is required maintain
the home at a temperature of 25°C, while it is constantly
losing heat to the surroundings at -5°C as shown in the diagram
above. We wish to determine the maximum possible Coefficient of
Performance (COPHP) that could be obtained
for an ideal heat pump operating under these conditions.
a) Choose the high and low temperatures for this evaluation, and
explain and justify your choice [268K, 298K].
b) Derive the equation for the maximum COPHP
starting with the basic definition of COPHP.
c) Evaluate the maximum possible COPHP [COPHP,max = 9.93], and state at least two reasons
why the actual heat pump system shown above cannot attain this
maximum.
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5. Fluid enters a throttling valve at 600 kPa and is throttled
to a pressure of 100 kPa. Calculate the drop in temperature as
well as the entropy generated by the process if a) the fluid is
refrigerant R134a and enters as a saturated liquid [DT = 48°C, sgen =
0.023 kJ/kg.K], and b) the fluid is helium and enters at
a temperature of 22°C [DT = 0°C, sgen = 3.723 kJ/kg.K].
Note: Assume that no heat transfer effects are occurring.
Justify all values used and derive all equations
used starting from the basic energy equation and total entropy
change (system and surroundings) for a flow system, as well as
the entropy change for an ideal gas.
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6. Consider a steam radiator used to heat a room. The radiator
has a volume of 15 L and is filled with superheated steam at 200
kPa and 200°C. At this moment both the inlet abd outlet valves
to the radiator are closed. Some time later the pressure of the
steam is observed to drop to 100 kPa due to the heat transfer
from the radiator to the room..
a) Sketch the process on a P-v diagram clearly indicating
the initial and final states with respect to critical point, saturation
lines, and the relevant constant temperature lines.
b) Determine the final temperature and quality of the steam (if
relevant) [T2 = 99.63°C, x2 = 0.637].
c) Determine the total amount of heat transfer from the radiator
to the room [12.59 kJ].
Justify all values used and derive all equations
used starting from the basic energy equation for a non-flow system.
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