1–1C How does the science of heat transfer differ from the
science of thermodynamics?
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1–2C What is the driving force for (a) heat transfer, (b) electric
current flow, and (c) fluid flow?
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1–3C What is the caloric theory? When and why was it
abandoned?
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1–4C How do rating problems in heat transfer differ from the
sizing problems?
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1–5C What is the difference between the analytical and experimental
approach to heat transfer? Discuss the advantages
and disadvantages of each approach.
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1–6C What is the importance of modeling in engineering?
How are the mathematical models for engineering processes
prepared?
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1–7C When modeling an engineering process, how is the
right choice made between a simple but crude and a complex
but accurate model? Is the complex model necessarily a better
choice since it is more accurate?
Heat and Other Forms of Energy
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1–8C What is heat flux? How is it related to the heat transfer
rate?
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1–9C What are the mechanisms of energy transfer to a closed
system? How is heat transfer distinguished from the other
forms of energy transfer?
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1–10C How are heat, internal energy, and thermal energy
related to each other?
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1–11C An ideal gas is heated from 50°C to 80°C (a) at constant
volume and (b) at constant pressure. For which case do
you think the energy required will be greater? Why?
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1–12 A cylindrical resistor element on a circuit board dissipates
0.6 W of power. The resistor is 1.5 cm long, and has a
diameter of 0.4 cm. Assuming heat to be transferred uniformly
from all surfaces, determine (a) the amount of heat this resistor
dissipates during a 24-hour period, (b) the heat flux, and (c) the
fraction of heat dissipated from the top and bottom surfaces.
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1–13E A logic chip used in a computer dissipates 3 W of
power in an environment at 120°F, and has a heat transfer surface
area of 0.08 in2. Assuming the heat transfer from the surface
to be uniform, determine (a) the amount of heat this chip
dissipates during an eight-hour work day, in kWh, and (b) the
heat flux on the surface of the chip, in W/in2.
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1–14 Consider a 150-W incandescent lamp. The filament
of the lamp is 5 cm long and has a diameter of 0.5 mm. The
diameter of the glass bulb of the lamp is 8 cm. Determine the
heat flux, in W/m2, (a) on the surface of the filament and (b) on
the surface of the glass bulb, and (c) calculate how much it will
cost per year to keep that lamp on for eight hours a day every
day if the unit cost of electricity is $0.08/kWh.
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1–15 A1200-W iron is left on the ironing board with its base
exposed to the air. About 90 percent of the heat generated
in the iron is dissipated through its base whose surface area is 150 cm2, and the remaining 10 percent through other surfaces.
Assuming the heat transfer from the surface to be uniform,determine (a) the amount of heat the iron dissipates during a
2-hour period, in kWh, (b) the heat flux on the surface of the
iron base, in W/m2, and (c) the total cost of the electrical energy
consumed during this 2-hour period. Take the unit cost of
electricity to be $0.07/kWh.
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1–16 A 15-cm x 20-cm circuit board houses on its surface 120 closely spaced logic chips, each dissipating 0.12 W. If the
heat transfer from the back surface of the board is negligible,
determine (a) the amount of heat this circuit board dissipates
during a 10-hour period, in kWh, and (b) the heat flux on the
surface of the circuit board, in W/m2.
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1–17 A 15-cm-diameter aluminum ball is to be heated from
80°C to an average temperature of 200°C. Taking the average
density and specific heat of aluminum in this temperature
range to be p= 2700 kg/m3 and Cp = 0.90 kJ/kg · °C, respectively,
determine the amount of energy that needs to be transferred
to the aluminum ball.
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1–18 The average specific heat of the human body is 3.6
kJ/kg · °C. If the body temperature of a 70-kg man rises from
37°C to 39°C during strenuous exercise, determine the increase
in the thermal energy content of the body as a result of this rise
in body temperature.
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1–19 Infiltration of cold air into a warm house during winter
through the cracks around doors, windows, and other openings
is a major source of energy loss since the cold air that enters
needs to be heated to the room temperature. The infiltration is
often expressed in terms of ACH (air changes per hour). An
ACH of 2 indicates that the entire air in the house is replaced
twice every hour by the cold air outside.
Consider an electrically heated house that has a floor space
of 200 m2 and an average height of 3 m at 1000 m elevation,
where the standard atmospheric pressure is 89.6 kPa. The
house is maintained at a temperature of 22°C, and the infiltration
losses are estimated to amount to 0.7 ACH. Assuming the
pressure and the temperature in the house remain constant, determine
the amount of energy loss from the house due to infiltration
for a day during which the average outdoor temperature
is 5°C. Also, determine the cost of this energy loss for that day
if the unit cost of electricity in that area is $0.082/kWh.
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1–20 Consider a house with a floor space of 200 m2 and an
average height of 3 m at sea level, where the standard atmospheric
pressure is 101.3 kPa. Initially the house is at a uniform
temperature of 10°C. Now the electric heater is turned on, and
the heater runs until the air temperature in the house rises to an
average value of 22°C. Determine how much heat is absorbed
by the air assuming some air escapes through the cracks as the
heated air in the house expands at constant pressure. Also, determine
the cost of this heat if the unit cost of electricity in that
area is $0.075/kWh.
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1–21E Consider a 60-gallon water heater that is initially
filled with water at 45°F. Determine how much energy needs to
be transferred to the water to raise its temperature to 140°F.
Take the density and specific heat of water to be 62 lbm/ft3 and 1.0 Btu/lbm · °F, respectively.
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1–22C On a hot summer day, a student turns his fan on when
he leaves his room in the morning. When he returns in the
evening, will his room be warmer or cooler than the neighboring
rooms? Why? Assume all the doors and windows are kept
closed.
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1–23C Consider two identical rooms, one with a refrigerator
in it and the other without one. If all the doors and windows are
closed, will the room that contains the refrigerator be cooler or
warmer than the other room? Why?
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1–24C Define mass and volume flow rates. How are they related
to each other?
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1–25 Two 800-kg cars moving at a velocity of 90 km/h have
a head-on collision on a road. Both cars come to a complete
rest after the crash. Assuming all the kinetic energy of cars is
converted to thermal energy, determine the average temperature
rise of the remains of the cars immediately after the crash.
Take the average specific heat of the cars to be 0.45 kJ/kg · °C.
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1–26 A classroom that normally contains 40 people is to be
air-conditioned using window air-conditioning units of 5-kW
cooling capacity. A person at rest may be assumed to dissipate
heat at a rate of 360 kJ/h. There are 10 lightbulbs in the room,
each with a rating of 100 W. The rate of heat transfer to the
classroom through the walls and the windows is estimated to
be 15,000 kJ/h. If the room air is to be maintained at a constant
temperature of 21°C, determine the number of window airconditioning
units required. Answer: two units
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1–27E A rigid tank contains 20 lbm of air at 50 psia and
80°F. The air is now heated until its pressure is doubled. Determine
(a) the volume of the tank and (b) the amount of heat transfer.
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1–28 A 1-m3 rigid tank contains hydrogen at 250 kPa and
420 K. The gas is now cooled until its temperature drops to 300
K. Determine (a) the final pressure in the tank and (b) the
amount of heat transfer from the tank.
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1–29 A 4-m x 5-m x 6-m room is to be heated by a baseboard
resistance heater. It is desired that the resistance heater
be able to raise the air temperature in the room from 7°C to
25°C within 15 minutes. Assuming no heat losses from the
room and an atmospheric pressure of 100 kPa, determine the
required power rating of the resistance heater. Assume constant
specific heats at room temperature.
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1–30 A 4-m x 5-m x 7-m room is heated by the radiator of
a steam heating system. The steam radiator transfers heat at a
rate of 10,000 kJ/h and a 100-W fan is used to distribute the
warm air in the room. The heat losses from the room are estimated
to be at a rate of about 5000 kJ/h. If the initial temperature
of the room air is 10°C, determine how long it will take for
the air temperature to rise to 20°C. Assume constant specific
heats at room temperature.
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1–31 A student living in a 4-m x 6-m x 6-m dormitory
room turns his 150-W fan on before she leaves her room on a
summer day hoping that the room will be cooler when she
comes back in the evening. Assuming all the doors and windows
are tightly closed and disregarding any heat transfer
through the walls and the windows, determine the temperature
in the room when she comes back 10 hours later. Use specific
heat values at room temperature and assume the room to be at 100 kPa and 15°C in the morning when she leaves.
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1–32E A 10-ft3 tank contains oxygen initially at 14.7 psia
and 80°F. A paddle wheel within the tank is rotated until the
pressure inside rises to 20 psia. During the process 20 Btu of
heat is lost to the surroundings. Neglecting the energy stored in
the paddle wheel, determine the work done by the paddle
wheel.
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1–33 A room is heated by a baseboard resistance heater.
When the heat losses from the room on a winter day amount to
7000 kJ/h, it is observed that the air temperature in the room
remains constant even though the heater operates continuously.
Determine the power rating of the heater, in kW.
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1–34 A 50-kg mass of copper at 70°C is dropped into an insulated
tank containing 80 kg of water at 25°C. Determine the
final equilibrium temperature in the tank.
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1–35 A 20-kg mass of iron at 100°C is brought into contact
with 20 kg of aluminum at 200°C in an insulated enclosure.
Determine the final equilibrium temperature of the combined
system.
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1–36 An unknown mass of iron at 90°C is dropped into an
insulated tank that contains 80 L of water at 20°C. At the same time, a paddle wheel driven by a 200-W motor is activated to
stir the water. Thermal equilibrium is established after 25 minutes
with a final temperature of 27°C. Determine the mass of
the iron. Neglect the energy stored in the paddle wheel, and
take the density of water to be 1000 kg/m3.
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1–37E A90-lbm mass of copper at 160°F and a 50-lbm mass
of iron at 200°F are dropped into a tank containing 180 lbm of
water at 70°F. If 600 Btu of heat is lost to the surroundings during
the process, determine the final equilibrium temperature.
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1–38 A 5-m x 6-m x 8-m room is to be heated by an electrical
resistance heater placed in a short duct in the room. Initially,
the room is at 15°C, and the local atmospheric pressure
is 98 kPa. The room is losing heat steadily to the outside at a
rate of 200 kJ/min. A 200-W fan circulates the air steadily
through the duct and the electric heater at an average mass flow
rate of 50 kg/min. The duct can be assumed to be adiabatic, and
there is no air leaking in or out of the room. If it takes 15 minutes
for the room air to reach an average temperature of 25°C,
find (a) the power rating of the electric heater and (b) the temperature
rise that the air experiences each time it passes
through the heater.
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1–39 A house has an electric heating system that consists of
a 300-W fan and an electric resistance heating element placed
in a duct. Air flows steadily through the duct at a rate of 0.6
kg/s and experiences a temperature rise of 5°C. The rate of heat
loss from the air in the duct is estimated to be 250 W. Determine
the power rating of the electric resistance heating
element.
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1–40 A hair dryer is basically a duct in which a few layers of
electric resistors are placed. A small fan pulls the air in and
forces it to flow over the resistors where it is heated. Air enters
a 1200-W hair dryer at 100 kPa and 22°C, and leaves at 47°C.
The cross-sectional area of the hair dryer at the exit is 60 cm2.
Neglecting the power consumed by the fan and the heat losses
through the walls of the hair dryer, determine (a) the volume
flow rate of air at the inlet and (b) the velocity of the air at the
exit.
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1–41 The ducts of an air heating system pass through an unheated
area. As a result of heat losses, the temperature of the air
in the duct drops by 3°C. If the mass flow rate of air is 120
kg/min, determine the rate of heat loss from the air to the cold
environment.
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1–42E Air enters the duct of an air-conditioning system at 15
psia and 50°F at a volume flow rate of 450 ft3/min. The diameter
of the duct is 10 inches and heat is transferred to the air in
the duct from the surroundings at a rate of 2 Btu/s. Determine
(a) the velocity of the air at the duct inlet and (b) the temperature
of the air at the exit.
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1–43 Water is heated in an insulated, constant diameter tube
by a 7-kW electric resistance heater. If the water enters the
heater steadily at 15°C and leaves at 70°C, determine the mass
flow rate of water.
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1–44C Define thermal conductivity and explain its significance
in heat transfer.
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1–45C What are the mechanisms of heat transfer? How are
they distinguished from each other?
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1–46C What is the physical mechanism of heat conduction in
a solid, a liquid, and a gas?
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1–47C Consider heat transfer through a windowless wall of
a house in a winter day. Discuss the parameters that affect the
rate of heat conduction through the wall.
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1–48C Write down the expressions for the physical laws that
govern each mode of heat transfer, and identify the variables
involved in each relation.
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1–49C How does heat conduction differ from convection?
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1–50C Does any of the energy of the sun reach the earth by
conduction or convection?
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1–51C How does forced convection differ from natural
convection?
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1–52C Define emissivity and absorptivity. What is Kirchhoff’s
law of radiation?
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1–53C What is a blackbody? How do real bodies differ from
blackbodies?
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1–54C Judging from its unit W/m · °C, can we define thermal
conductivity of a material as the rate of heat transfer
through the material per unit thickness per unit temperature
difference? Explain.
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1–55C Consider heat loss through the two walls of a house
on a winter night. The walls are identical, except that one of
them has a tightly fit glass window. Through which wall will
the house lose more heat? Explain.
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1–56C Which is a better heat conductor, diamond or silver?
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1–57C Consider two walls of a house that are identical except
that one is made of 10-cm-thick wood, while the other is
made of 25-cm-thick brick. Through which wall will the house
lose more heat in winter?
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1–58C How do the thermal conductivity of gases and liquids
vary with temperature?
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1–59C Why is the thermal conductivity of superinsulation
orders of magnitude lower than the thermal conductivity of
ordinary insulation?
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1–60C Why do we characterize the heat conduction ability
of insulators in terms of their apparent thermal conductivity
instead of the ordinary thermal conductivity?
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1–61C Consider an alloy of two metals whose thermal conductivities
are k1 and k2. Will the thermal conductivity of the
alloy be less than k1, greater than k2, or between k1 and k2?
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1–62 The inner and outer surfaces of a 5-m x 6-m brick wall
of thickness 30 cm and thermal conductivity 0.69 W/m · °C are
maintained at temperatures of 20°C and 5°C, respectively.
Determine the rate of heat transfer through the wall, in W.
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1–63
The inner and outer surfaces of a 0.5-cm-thick 2-m x 2-m window glass
in winter are 10°C and 3°C, respectively. If the thermal conductivity of
the glass is 0.78 W/m · °C, determine
the amount of heat loss, in kJ, through the glass over a
period of 5 hours. What would your answer be if the glass were 1 cm
thick?
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1–64 Reconsider Problem 1–63. Using EES (or other)
software, plot the amount of heat loss through the
glass as a function of the window glass thickness in the range
of 0.1 cm to 1.0 cm. Discuss the results.
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1–65 An aluminum pan whose thermal conductivity is
237 W/m · °C has a flat bottom with diameter 20 cm and thickness
0.4 cm. Heat is transferred steadily to boiling water in the
pan through its bottom at a rate of 800 W. If the inner surface
of the bottom of the pan is at 105°C, determine the temperature
of the outer surface of the bottom of the pan.
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1–66E The north wall of an electrically heated home is 20 ft
long, 10 ft high, and 1 ft thick, and is made of brick whose
thermal conductivity is k = 0.42 Btu/h · ft · °F. On a certain
winter night, the temperatures of the inner and the outer surfaces
of the wall are measured to be at about 62°F and 25°F,
respectively, for a period of 8 hours. Determine (a) the rate of
heat loss through the wall that night and (b) the cost of that heat
loss to the home owner if the cost of electricity is $0.07/kWh.
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1–67 In a certain experiment, cylindrical samples of diameter
4 cm and length 7 cm are used (see Fig. 1–29). The two
thermocouples in each sample are placed 3 cm apart. After initial
transients, the electric heater is observed to draw 0.6 A at 110 V, and both differential thermometers read a temperature
difference of 10°C. Determine the thermal conductivity of the
sample.
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1–68 One way of measuring the thermal conductivity of a
material is to sandwich an electric thermofoil heater between
two identical rectangular samples of the material and to heavily
insulate the four outer edges, as shown in the figure. Thermocouples
attached to the inner and outer surfaces of the samples
record the temperatures.
During an experiment, two 0.5-cm-thick samples 10 cm x 10 cm in size are used. When steady operation is reached, the
heater is observed to draw 35Wof electric power, and the temperature
of each sample is observed to drop from 82°C at the
inner surface to 74°C at the outer surface. Determine the thermal
conductivity of the material at the average temperature.
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1–69 Repeat Problem 1–68 for an electric power consumption
of 28 W.
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1–70 A heat flux meter attached to the inner surface of a
3-cm-thick refrigerator door indicates a heat flux of 25 W/m2
through the door. Also, the temperatures of the inner and the
outer surfaces of the door are measured to be 7°C and 15°C,
respectively. Determine the average thermal conductivity of
the refrigerator door.
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1–71 Consider a person standing in a room maintained at
20°C at all times. The inner surfaces of the walls, floors, and
ceiling of the house are observed to be at an average temperature
of 12°C in winter and 23°C in summer. Determine the
rates of radiation heat transfer between this person and the surrounding
surfaces in both summer and winter if the exposed
surface area, emissivity, and the average outer surface temperature
of the person are 1.6 m2, 0.95, and 32°C, respectively.
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1–72 Reconsider Problem 1–71. Using EES (or other)
software, plot the rate of radiation heat transfer in
winter as a function of the temperature of the inner surface of
the room in the range of 8°C to 18°C. Discuss the results.
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1–73 For heat transfer purposes, a standing man can be modeled
as a 30-cm-diameter, 170-cm-long vertical cylinder with
both the top and bottom surfaces insulated and with the side
surface at an average temperature of 34°C. For a convection
heat transfer coefficient of 15 W/m2 · °C, determine the rate of
heat loss from this man by convection in an environment at
20°C.
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1–74 Hot air at 80°C is blown over a 2-m x 4-m flat surface
at 30°C. If the average convection heat transfer coefficient is
55 W/m2 · °C, determine the rate of heat transfer from the air to
the plate, in kW.
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1–75 Reconsider Problem 1–74. Using EES (or other)
software, plot the rate of heat transfer as a function
of the heat transfer coefficient in the range of 20 W/m2 · °C
to 100 W/m2 · °C. Discuss the results.
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1–76 The heat generated in the circuitry on the surface of a
silicon chip (k = 130 W/m · °C) is conducted to the ceramic
substrate to which it is attached. The chip is 6 mm x 6 mm in
size and 0.5 mm thick and dissipates 3Wof power. Disregarding
any heat transfer through the 0.5-mm-high side surfaces,
determine the temperature difference between the front and
back surfaces of the chip in steady operation.
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1–77 A 50-cm-long, 800-W electric resistance heating element
with diameter 0.5 cm and surface temperature 120°C is
immersed in 60 kg of water initially at 20°C. Determine how
long it will take for this heater to raise the water temperature to
80°C. Also, determine the convection heat transfer coefficients
at the beginning and at the end of the heating process.
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1–78 A 5-cm-external-diameter, 10-m-long hot water pipe at
80°C is losing heat to the surrounding air at 5°C by natural
convection with a heat transfer coefficient of 25 W/m2 · °C.
Determine the rate of heat loss from the pipe by natural convection,
in W. Answer: 2945 W
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1–79 A hollow spherical iron container with outer diameter
20 cm and thickness 0.4 cm is filled with iced water at 0°C. If
the outer surface temperature is 5°C, determine the approximate
rate of heat loss from the sphere, in kW, and the rate at
which ice melts in the container. The heat from fusion of water
is 333.7 kJ/kg.
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1–80 Reconsider Problem 1–79. Using EES (or other)
software, plot the rate at which ice melts as a
function of the container thickness in the range of 0.2 cm to
2.0 cm. Discuss the results.
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1–81E The inner and outer glasses of a 6-ft x 6-ft doublepane
window are at 60°F and 42°F, respectively. If the 0.25-in.
space between the two glasses is filled with still air, determine
the rate of heat transfer through the window.
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1–82 Two surfaces of a 2-cm-thick plate are maintained at
0°C and 80°C, respectively. If it is determined that heat is
transferred through the plate at a rate of 500 W/m2, determine
its thermal conductivity.
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1–83 Four power transistors, each dissipating 15 W, are
mounted on a thin vertical aluminum plate 22 cm x 22 cm in
size. The heat generated by the transistors is to be dissipated by
both surfaces of the plate to the surrounding air at 25°C, which
is blown over the plate by a fan. The entire plate can be assumed
to be nearly isothermal, and the exposed surface area of
the transistor can be taken to be equal to its base area. If the
average convection heat transfer coefficient is 25 W/m2 · °C,
determine the temperature of the aluminum plate. Disregard
any radiation effects.
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1–84 An ice chest whose outer dimensions are 30 cm x
40 cm x 40 cm is made of 3-cm-thick Styrofoam (k x 0.033
W/m · °C). Initially, the chest is filled with 40 kg of ice at 0°C,
and the inner surface temperature of the ice chest can be taken
to be 0°C at all times. The heat of fusion of ice at 0°C is 333.7
kJ/kg, and the surrounding ambient air is at 30°C. Disregarding
any heat transfer from the 40-cm x 40-cm base of the ice
chest, determine how long it will take for the ice in the chest to
melt completely if the outer surfaces of the ice chest are at 8°C.
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1–85 A transistor with a height of 0.4 cm and a diameter of
0.6 cm is mounted on a circuit board. The transistor is cooled
by air flowing over it with an average heat transfer coefficient
of 30 W/m2 · °C. If the air temperature is 55°C and the transistor
case temperature is not to exceed 70°C, determine the
amount of power this transistor can dissipate safely. Disregard
any heat transfer from the transistor base.
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1–86 Reconsider Problem 1–85. Using EES (or other)
software, plot the amount of power the transistor
can dissipate safely as a function of the maximum case temperature
in the range of 60°C to 90°C. Discuss the results.
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1–87E A 200-ft-long section of a steam pipe whose outer diameter
is 4 inches passes through an open space at 50°F. The
average temperature of the outer surface of the pipe is measured
to be 280°F, and the average heat transfer coefficient on
that surface is determined to be 6 Btu/h · ft2 · °F. Determine
(a) the rate of heat loss from the steam pipe and (b) the annual
cost of this energy loss if steam is generated in a natural gas
furnace having an efficiency of 86 percent, and the price of natural
gas is $0.58/therm (1 therm = 100,000 Btu).
Answers: (a) 289,000 Btu/h, (b) $17,074/yr
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1–88 The boiling temperature of nitrogen at atmospheric
pressure at sea level (1 atm) is -196°C. Therefore, nitrogen is
commonly used in low temperature scientific studies since the
temperature of liquid nitrogen in a tank open to the atmosphere
will remain constant at -196°C until the liquid nitrogen in
the tank is depleted. Any heat transfer to the tank will result
in the evaporation of some liquid nitrogen, which has a heat of
vaporization of 198 kJ/kg and a density of 810 kg/m3 at 1 atm.
Consider a 4-m-diameter spherical tank initially filled
with liquid nitrogen at 1 atm and -196°C. The tank is exposed
to 20°C ambient air with a heat transfer coefficient of
25 W/m2 · °C. The temperature of the thin-shelled spherical
tank is observed to be almost the same as the temperature of
the nitrogen inside. Disregarding any radiation heat exchange,
determine the rate of evaporation of the liquid nitrogen in the
tank as a result of the heat transfer from the ambient air.
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1–89 Repeat Problem 1–88 for liquid oxygen, which has
a boiling temperature of -183°C, a heat of vaporization of
213 kJ/kg, and a density of 1140 kg/m3 at 1 atm pressure.
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1–90 Reconsider Problem 1–88. Using EES (or other)
software, plot the rate of evaporation of liquid
nitrogen as a function of the ambient air temperature in the
range of 0°C to 35°C. Discuss the results.
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1–91 Consider a person whose exposed surface area is 1.7 m2, emissivity is 0.7, and surface temperature is 32°C.
Determine the rate of heat loss from that person by radiation in
a large room having walls at a temperature of (a) 300 K and
(b) 280 K. Answers: (a) 37.4 W, (b) 169.2 W
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1–92 A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit
board houses 80 closely spaced logic chips on one side, each
dissipating 0.06 W. The board is impregnated with copper fillings
and has an effective thermal conductivity of 16 W/m · °C.
All the heat generated in the chips is conducted across the circuit
board and is dissipated from the back side of the board to
the ambient air. Determine the temperature difference between
the two sides of the circuit board. Answer: 0.042°C
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1–93 Consider a sealed 20-cm-high electronic box whose
base dimensions are 40 cm x 40 cm placed in a vacuum chamber.
The emissivity of the outer surface of the box is 0.95. If the
electronic components in the box dissipate a total of 100 W of
power and the outer surface temperature of the box is not to exceed
55°C, determine the temperature at which the surrounding
surfaces must be kept if this box is to be cooled by radiation
alone. Assume the heat transfer from the bottom surface of the
box to the stand to be negligible.
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1–94 Using the conversion factors between W and Btu/h, m
and ft, and K and R, express the Stefan–Boltzmann constant
o= 5.67 x 10-8 W/m2 · K4 in the English unit Btu/h · ft2 · R4.
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1–95 An engineer who is working on the heat transfer analysis
of a house in English units needs the convection heat transfer
coefficient on the outer surface of the house. But the only
value he can find from his handbooks is 20 W/m2 · °C, which
is in SI units. The engineer does not have a direct conversion
factor between the two unit systems for the convection heat
transfer coefficient. Using the conversion factors between
W and Btu/h, m and ft, and °C and °F, express the given convection
heat transfer coefficient in Btu/h · ft2 · °F.
Simultaneous Heat Transfer Mechanisms
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1–96C Can all three modes of heat transfer occur simultaneously
(in parallel) in a medium?
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1–97C Can a medium involve (a) conduction and convection,
(b) conduction and radiation, or (c) convection and radiation
simultaneously? Give examples for the “yes” answers.
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1–98C The deep human body temperature of a healthy
person remains constant at 37°C while the temperature and
the humidity of the environment change with time. Discuss the
heat transfer mechanisms between the human body and the environment
both in summer and winter, and explain how a person
can keep cooler in summer and warmer in winter.
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1–99C We often turn the fan on in summer to help us cool.
Explain how a fan makes us feel cooler in the summer. Also
explain why some people use ceiling fans also in winter.
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1–100 Consider a person standing in a room at 23°C. Determine
the total rate of heat transfer from this person if the exposed
surface area and the skin temperature of the person are
1.7 m2 and 32°C, respectively, and the convection heat transfer
coefficient is 5 W/m2 · °C. Take the emissivity of the skin and
the clothes to be 0.9, and assume the temperature of the inner
surfaces of the room to be the same as the air temperature.
Answer: 161 W
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1–101 Consider steady heat transfer between two large
parallel plates at constant temperatures of T1 = 290 K and
T2 = 150 K that are L = 2 cm apart. Assuming the surfaces to
be black (emissivity e= 1), determine the rate of heat transfer
between the plates per unit surface area assuming the gap
between the plates is (a) filled with atmospheric air, (b) evacuated,
(c) filled with fiberglass insulation, and (d) filled with
superinsulation having an apparent thermal conductivity of
0.00015 W/m · °C.
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1–102 A1.4-m-long, 0.2-cm-diameter electrical wire extends
across a room that is maintained at 20°C. Heat is generated in
the wire as a result of resistance heating, and the surface temperature
of the wire is measured to be 240°C in steady operation.
Also, the voltage drop and electric current through
the wire are measured to be 110 V and 3 A, respectively. Disregarding
any heat transfer by radiation, determine the convection
heat transfer coefficient for heat transfer between the
outer surface of the wire and the air in the room.
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1–103 Reconsider Problem 1–102. Using EES (or
other) software, plot the convection heat transfer
coefficient as a function of the wire surface temperature in
the range of 100°C to 300°C. Discuss the results.
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1–104E A 2-in-diameter spherical ball whose surface is
maintained at a temperature of 170°F is suspended in the middle
of a room at 70°F. If the convection heat transfer coefficient
is 12 Btu/h · ft2 · °F and the emissivity of the surface is 0.8, determine
the total rate of heat transfer from the ball.
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1–105 A 1000-W iron is left on the iron board with its
base exposed to the air at 20°C. The convection
heat transfer coefficient between the base surface and the surrounding
air is 35 W/m2 · °C. If the base has an emissivity of
0.6 and a surface area of 0.02 m2, determine the temperature of
the base of the iron.
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1–106 The outer surface of a spacecraft in space has an emissivity
of 0.8 and a solar absorptivity of 0.3. If solar radiation is
incident on the spacecraft at a rate of 950 W/m2, determine the
surface temperature of the spacecraft when the radiation emitted
equals the solar energy absorbed.
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1–107 A3-m-internal-diameter spherical tank made of 1-cmthick
stainless steel is used to store iced water at 0°C. The tank
is located outdoors at 25°C. Assuming the entire steel tank to
be at 0°C and thus the thermal resistance of the tank to be negligible,
determine (a) the rate of heat transfer to the iced water
in the tank and (b) the amount of ice at 0°C that melts during a
24-hour period. The heat of fusion of water at atmospheric pressure
is hif = 333.7 kJ/kg. The emissivity of the outer surface of
the tank is 0.6, and the convection heat transfer coefficient on
the outer surface can be taken to be 30 W/m2 · °C. Assume the
average surrounding surface temperature for radiation exchange
to be 15°C.
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1–108 The roof of a house consists of a 15-cm-thick
concrete slab (k = 2 W/m · °C) that is 15 m
wide and 20 m long. The emissivity of the outer surface of the
roof is 0.9, and the convection heat transfer coefficient on that
surface is estimated to be 15 W/m2 · °C. The inner surface of
the roof is maintained at 15°C. On a clear winter night, the ambient
air is reported to be at 10°C while the night sky temperature
for radiation heat transfer is 255 K. Considering both
radiation and convection heat transfer, determine the outer surface
temperature and the rate of heat transfer through the roof.
If the house is heated by a furnace burning natural gas with
an efficiency of 85 percent, and the unit cost of natural gas is
$0.60/therm (1 therm = 105,500 kJ of energy content), determine
the money lost through the roof that night during a
14-hour period.
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1–109E Consider a flat plate solar collector placed horizontally
on the flat roof of a house. The collector is 5 ft wide and
15 ft long, and the average temperature of the exposed surface of the collector is 100°F. The emissivity of the exposed surface
of the collector is 0.9. Determine the rate of heat loss from
the collector by convection and radiation during a calm day
when the ambient air temperature is 70°F and the effective
sky temperature for radiation exchange is 50°F. Take the convection
heat transfer coefficient on the exposed surface to be
2.5 Btu/h · ft2 · °F.
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1–110C What is the value of the engineering software packages
in (a) engineering education and (b) engineering practice?
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1–111 Determine a positive real root of the following
equation using EES:
2x3 - 10x0.5 - 3x =-3
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1–112 Solve the following system of two equations
with two unknowns using EES:
x3 - y2 = 7.75
3xy + y = 3.5
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1–113 Solve the following system of three equations
with three unknowns using EES:
2x - y + z = 5
3x2 + 2y = z + 2
xy + 2z = 8
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1–114 Solve the following system of three equations
with three unknowns using EES:
x2y - z = 1
x - 3y0.5 + xz=-2
x + y - z = 2
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1–115C What is metabolism? What is the range of metabolic
rate for an average man? Why are we interested in metabolic rate of the occupants of a building when we deal with heating
and air conditioning?
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1–116C Why is the metabolic rate of women, in general,
lower than that of men? What is the effect of clothing on the
environmental temperature that feels comfortable?
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1–117C What is asymmetric thermal radiation? How does it
cause thermal discomfort in the occupants of a room?
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1–118C How do (a) draft and (b) cold floor surfaces cause
discomfort for a room’s occupants?
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1–119C What is stratification? Is it likely to occur at places
with low or high ceilings? How does it cause thermal discomfort
for a room’s occupants? How can stratification be prevented?
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1–120C Why is it necessary to ventilate buildings? What is
the effect of ventilation on energy consumption for heating in
winter and for cooling in summer? Is it a good idea to keep the
bathroom fans on all the time? Explain.
Review Problems
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1–121 2.5 kg of liquid water initially at 18°C is to be heated
to 96°C in a teapot equipped with a 1200-W electric heating
element inside. The teapot is 0.8 kg and has an average specific
heat of 0.6 kJ/kg · °C. Taking the specific heat of water to be
4.18 kJ/kg · °C and disregarding any heat loss from the teapot,
determine how long it will take for the water to be heated.
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1–122 A4-m-long section of an air heating system of a house
passes through an unheated space in the attic. The inner diameter
of the circular duct of the heating system is 20 cm. Hot air
enters the duct at 100 kPa and 65°C at an average velocity of
3 m/s. The temperature of the air in the duct drops to 60°C as a
result of heat loss to the cool space in the attic. Determine the
rate of heat loss from the air in the duct to the attic under steady
conditions. Also, determine the cost of this heat loss per hour if
the house is heated by a natural gas furnace having an efficiency
of 82 percent, and the cost of the natural gas in that area
is $0.58/therm (1 therm = 105,500 kJ).
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1–123 Reconsider Problem 1–122. Using EES (or
other) software, plot the cost of the heat loss per
hour as a function of the average air velocity in the range of
1 m/s to 10 m/s. Discuss the results.
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1–124 Water flows through a shower head steadily at a rate
of 10 L/min. An electric resistance heater placed in the water
pipe heats the water from 16°C to 43°C. Taking the density of water to be 1 kg/L, determine the electric power input to the
heater, in kW.
In an effort to conserve energy, it is proposed to pass the
drained warm water at a temperature of 39°C through a heat
exchanger to preheat the incoming cold water. If the heat exchanger
has an effectiveness of 0.50 (that is, it recovers only
half of the energy that can possibly be transferred from the
drained water to incoming cold water), determine the electric
power input required in this case. If the price of the electric energy
is 8.5 ¢/kWh, determine how much money is saved during
a 10-minute shower as a result of installing this heat exchanger.
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1–125 It is proposed to have a water heater that consists of an
insulated pipe of 5 cm diameter and an electrical resistor inside.
Cold water at 15°C enters the heating section steadily at a
rate of 18 L/min. If water is to be heated to 50°C, determine
(a) the power rating of the resistance heater and (b) the average
velocity of the water in the pipe.
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1–126 A passive solar house that is losing heat to the outdoors
at an average rate of 50,000 kJ/h is maintained at 22°C at
all times during a winter night for 10 hours. The house is to be
heated by 50 glass containers each containing 20 L of water
heated to 80°C during the day by absorbing solar energy.
A thermostat-controlled 15-kW back-up electric resistance
heater turns on whenever necessary to keep the house at 22°C.
(a) How long did the electric heating system run that night?
(b) How long would the electric heater have run that night if
the house incorporated no solar heating?
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1–127 It is well known that wind makes the cold air feel
much colder as a result of the windchill effect that is due to the
increase in the convection heat transfer coefficient with increasing
air velocity. The windchill effect is usually expressed
in terms of the windchill factor, which is the difference between
the actual air temperature and the equivalent calm-air temperature. For example, a windchill factor of 20°C for an
actual air temperature of 5°C means that the windy air at 5°C
feels as cold as the still air at -15°C. In other words, a person
will lose as much heat to air at 5°C with a windchill factor of
20°C as he or she would in calm air at -15°C.
For heat transfer purposes, a standing man can be modeled
as a 30-cm-diameter, 170-cm-long vertical cylinder with both
the top and bottom surfaces insulated and with the side surface
at an average temperature of 34°C. For a convection heat transfer
coefficient of 15 W/m2 · °C, determine the rate of heat loss
from this man by convection in still air at 20°C. What would
your answer be if the convection heat transfer coefficient is increased
to 50 W/m2 · °C as a result of winds? What is the windchill
factor in this case? Answers: 336 W, 1120 W, 32.7°C
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1–128 A thin metal plate is insulated on the back and exposed
to solar radiation on the front surface. The exposed surface
of the plate has an absorptivity of 0.7 for solar radiation. If
solar radiation is incident on the plate at a rate of 700 W/m2
and the surrounding air temperature is 10°C, determine the surface
temperature of the plate when the heat loss by convection
equals the solar energy absorbed by the plate. Take the convection
heat transfer coefficient to be 30 W/m2 · °C, and disregard
any heat loss by radiation.
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1–129 A 4-m x 5-m x 6-m room is to be heated by one ton
(1000 kg) of liquid water contained in a tank placed in the
room. The room is losing heat to the outside at an average rate
of 10,000 kJ/h. The room is initially at 20°C and 100 kPa, and
is maintained at an average temperature of 20°C at all times. If
the hot water is to meet the heating requirements of this room
for a 24-hour period, determine the minimum temperature of
the water when it is first brought into the room. Assume constant
specific heats for both air and water at room temperature.
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1–130 Consider a 3-m x 3-m x 3-m cubical furnace whose
top and side surfaces closely approximate black surfaces at a
temperature of 1200 K. The base surface has an emissivity of
e= 0.7, and is maintained at 800 K. Determine the net rate
of radiation heat transfer to the base surface from the top and
side surfaces.
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1–131 Consider a refrigerator whose dimensions are 1.8 m x
1.2 m x 0.8 m and whose walls are 3 cm thick. The refrigerator
consumes 600 W of power when operating and has a COP
of 2.5. It is observed that the motor of the refrigerator remains
on for 5 minutes and then is off for 15 minutes periodically. If
the average temperatures at the inner and outer surfaces of the
refrigerator are 6°C and 17°C, respectively, determine the average
thermal conductivity of the refrigerator walls. Also, determine
the annual cost of operating this refrigerator if the unit
cost of electricity is $0.08/kWh.
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1–132 A 0.2-L glass of water at 20°C is to be cooled with
ice to 5°C. Determine how much ice needs to be added to
the water, in grams, if the ice is at 0°C. Also, determine how
much water would be needed if the cooling is to be done with
cold water at 0°C. The melting temperature and the heat of
fusion of ice at atmospheric pressure are 0°C and 333.7 kJ/kg,
respectively, and the density of water is 1 kg/L.
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1–133 Reconsider Problem 1–132. Using EES (or
other) software, plot the amount of ice that
needs to be added to the water as a function of the ice temperature
in the range of -24°C to 0°C. Discuss the results.
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1–134E In order to cool 1 short ton (2000 lbm) of water at
70°F in a tank, a person pours 160 lbm of ice at 25°F into the
water. Determine the final equilibrium temperature in the tank.
The melting temperature and the heat of fusion of ice at atmospheric
pressure are 32°F and 143.5 Btu/lbm, respectively.
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1–135 Engine valves (Cp = 440 J/kg · °C and p= 7840
kg/m3) are to be heated from 40°C to 800°C in 5 minutes in the
heat treatment section of a valve manufacturing facility. The
valves have a cylindrical stem with a diameter of 8 mm and a
length of 10 cm. The valve head and the stem may be assumed
to be of equal surface area, with a total mass of 0.0788 kg. For
a single valve, determine (a) the amount of heat transfer,
(b) the average rate of heat transfer, and (c) the average heat
flux, (d) the number of valves that can be heat treated per day if
the heating section can hold 25 valves, and it is used 10 hours
per day.
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1–136 The hot water needs of a household are met by an
electric 60-L hot water tank equipped with a 1.6-kW heating
element. The tank is initially filled with hot water at 80°C, and
the cold water temperature is 20°C. Someone takes a shower
by mixing constant flow rates of hot and cold waters. After a
showering period of 8 minutes, the average water temperature
in the tank is measured to be 60°C. The heater is kept on during
the shower and hot water is replaced by cold water. If the cold
water is mixed with the hot water stream at a rate of 0.06 kg/s,
determine the flow rate of hot water and the average temperature
of mixed water used during the shower.
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1–137 Consider a flat plate solar collector placed at the roof
of a house. The temperatures at the inner and outer surfaces of
glass cover are measured to be 28°C and 25°C, respectively.
The glass cover has a surface area of 2.2. m2 and a thickness of
0.6 cm and a thermal conductivity of 0.7 W/m · C. Heat is lost
from the outer surface of the cover by convection and radiation
with a convection heat transfer coefficient of 10 W/m2 · °C and
an ambient temperature of 15°C. Determine the fraction of heat
lost from the glass cover by radiation.
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1–138 The rate of heat loss through a unit surface area of
a window per unit temperature difference between the indoors
and the outdoors is called the U-factor. The value of
the U-factor ranges from about 1.25 W/m2 · °C (or 0.22
Btu/h · ft2 · °F) for low-e coated, argon-filled, quadruple-pane
windows to 6.25 W/m2 · °C (or 1.1 Btu/h · ft2 · °F) for a singlepane
window with aluminum frames. Determine the range for
the rate of heat loss through a 1.2-m x 1.8-m window of a
house that is maintained at 20°C when the outdoor air temperature
is -8°C.
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1–139 Reconsider Problem 1–138. Using EES (or
other) software, plot the rate of heat loss
through the window as a function of the U-factor. Discuss
the results.
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