Chapter 

17 – Temperature and Heat 
Problem 17.1*
a. A metal object has length and linear expansion coefficient . When the temperature
increases from to , what is the change ∆ in length of the object?
b. The Humber Bridge in England has the world’s longest single span of length
1410 m. Calculate the change ∆ in length of the steel deck of the span when the
temperature increases from 6.0 to 17.5 , knowing that steel has a linear
expansion coefficient 1.2 10 K .

Problem 17.2*
In an effort to stay awake for an all-night study session, a student makes a cup of coffee by
first placing an electric immersion heater with power in water of mass with specific heat
.
a. How much heat ( ) must be added to the water to raise its temperature from to ?
b. How much time ∆ is required? Assume that all of the heater’s power goes into heating
the water.
c. Calculate the amount of heat when 4190 J/kg ⋅ K, 0.400 kg, 21.0 ,
and 90.5 , and 200 W. Also calculate the required time ∆ .

Problem 17.3*
In very cold weather a significant mechanism for heat loss by the human body is energy
expended in warming the air taken into the lungs with each breath.
a. On a cold winter day the temperature is . Each breath takes in a volume of air. How
much heat is needed to warm this air to body temperature ? Assume that the specific
heat of air is and that air has density (mass per unit volume). Give a symbolic
expression
i. Next calculate the amount of heat using 20 , 37 , 0.50 l,
1020 J/kg ⋅ K, and 1.3 10 kg/l.
b. How much heat is lost per hour if the respiration rate is breaths per minute? Give a
symbolic expression.
i. Calculate the amount of heat using 20 and using the results of (a) sub (i).

Problem 17.4**
An open container holds mass of ice at . The mass of the container can be ignored. Heat
is supplied to the container at the constant rate of for time ∆ . The specific heat of ice is i ,
the heat of fusion is f , and the melting temperature of ice is melt .
a. After how many minutes does the ice start to melt?
b. How many more minutes does it take for the temperature to rise above the melting point
of ice?

3NBB0 ‐ Chapter 17 – Temperature and Heat 
Figures adapted from Young and Freedman, University Physics ed.12 
c. Plot a curve showing the temperature as a function of the elapsed time (a scale is not
needed)
d. Calculate the results of (a) and (b) using 0.550 kg, 15.0 , melt 0.00 ,
800.0 J/min, ∆ 500.0 min, i 2100 J/kg ⋅ K, f 334 10 J/kg.

Problem 17.5**
A carpenter builds an exterior house wall with a layer of wood with thickness w on the
outside and a layer of Styrofoam insulation with thickness s on the inside wall surface. The
wood and the Styrofoam have a thermal conductivity w and s respectively. The interior
surface temperature is int , and the exterior surface temperature is ext .
a. What is the temperature at the plane where the wood meets the Styrofoam?
b. What is the rate of heat flow per square meter through this wall?
c. Calculate the results of (a) and (b) using w 3.1 cm, s 2.4 cm, w 0.080 W/m ⋅
K, s 0.01 W/m ⋅ K, int 19.0 , and ext 12.0 .

Problem 17.6*
An electric kitchen range has a total wall area and is insulated with a layer of fiberglass of
thickness fiber . The inside surface of the fiberglass has a temperature of in , and its outside
surface is at out . The fiberglass has a thermal conductivity fiber .
a. What is the heat current through the insulation, assuming it may be treated as a flat slab
with an area ?
b. What electric-power input to the heating element is required to maintain this
temperature?
c. Calculate the results of (a) and (b) using 1.40 m , fiber 4.00 cm, fiber
0.040 W/m ⋅ K, in 175 , and out 35.0 .

Problem 17.7**
A picture window (a window containing one large sheet of glass) has area and is made of
glass with thickness g and thermal conductivity g . On a winter day, the temperature of the
outside surface of the glass is out , while the temperature of the inside surface is in .
a. At what rate is heat being lost through the window by conduction?
b. At what rate would heat be lost through the window if you covered it with a layer of
paper of thickness p and thermal conductivity p ?
c. Calculate the results of (a) and (b) when the dimension of the window is 1.40 m
2.50 m, g 6.00 mm, g 0.80 W/m ⋅ K, out 17.0 , and in 21.0 , p
0.750 mm, and p 0.0500 W/m ⋅ K.

3NBB0 ‐ Chapter 17 – Temperature and Heat 
Figures adapted from Young and Freedman, University Physics ed.12 
Problem 17.8*
The operating temperature of a tungsten filament in an incandescent light bulb is t, and its
emissivity is t .
a. Find the surface area of the filament of a bulb with power if all the electrical energy
consumed by the bulb is radiated by the filament as electromagnetic waves. (Only a
fraction of the radiation appears as visible light.)
b. Calculate using t 2500 K, t 0.350, and 200 W.

Problem 17.9**
A metal rod that has a length expands by ∆ when its temperature is raised from to .
A rod of a different metal and of the same length expands by ∆ for the same rise in
temperature. A third rod, also of length , is made up of pieces of each of the above metals
placed end to end and expands ∆ between the same rise in temperature.
a. Find the length and of each portion of the composite rod.
b. Calculate and using 31.0 cm, ∆ 6.80 10 cm, ∆ 3.10 10 cm,
∆ 5.00 10 cm, 0.0 , and 100.0 .

Problem 17.10*
a. A typical student listening attentively to a physics lecture has a heat output . How
much heat energy does a class of physics students release into a lecture hall over the
course of lecture of time ∆ ?
b. Assume that all the heat energy in part (a) is transferred to the air, which occupies volume
, in the room. The air has specific heat air and density air . If none of the heat escapes
and the air conditioning system is off, how much will the temperature of the air in the
room rise during the lecture?
c. If the student is taking an exam, the heat output rises to . What is the temperature rise
during time ∆ in this case?
d. Calculate the results of (a), (b), and (c) using 110 W, 300 W, 85, ∆
50 min, 4000 m , air 1020 J/kg ⋅ K, and air 1.20 kg/m .

Problem 17.11**
Animals in cold climates often depend on two layers of insulation: a layer of body fat (of
thermal conductivity ) surrounded by a layer of air (thermal conductivity ) trapped inside
fur or down. We can model a black bear (Ursus americanus) as a sphere with diameter
having a layer of fat which is thick. (Actually, the thickness varies with the season, but we
are interested in hibernation, when the fat layer is thickest.) In studies of bear hibernation, it
was found that the outer surface layer of the fur is at during hibernation, while the inner
surface of the fat layer is at .

3NBB0 ‐ Chapter 17 – Temperature and Heat 
Figures adapted from Young and Freedman, University Physics ed.12 
a. What is the temperature at the fat– inner fur boundary so that the bear loses heat at a rate
?
b. How thick should the air layer (contained within the fur) be?
c. Calculate the results of (a) and (b) using 0.20 W/m ⋅ K, 0.024 W/m ⋅ K,
1.5 m, 3.90 cm, 2.90 , 31.3 , and 50.8 W.

Problem 17.12**
In a household hot-water heating system, water is delivered to the radiators at in and leaves
at out, . The system is to be replaced by a steam system in which steam at atmospheric
pressure condenses in the radiators and the condensed steam leaves the radiators at out, .
a. How much steam (in mass s ) will supply the same heat as was supplied by a mass w
of hot water in the first system?
b. Calculate s using in 70.0 , out, 28.0 , out, 35.0 , and w 1.00 kg.

Problem 17.13*
A Styrofoam bucket of negligible mass contains water of mass and ice of mass . More
ice, from a refrigerator at temperature , is added to the mixture in the bucket, and when
thermal equilibrium has been reached, the total mass of ice in the bucket is .

a. Assuming no heat exchange with the surroundings, what mass of ice was added?
b. Calcultate the result of (a) using 1.75 kg, 0.450 kg, 15.0 , and
0.884 kg.

Problem 17.14**
One experimental method of measuring an insulating material’s thermal conductivity is to
construct a box of the material and measure the power input to an electric heater inside the
box that maintains the interior at a measured temperature above the outside surface. Suppose
that in such an apparatus a power input is required to keep the interior surface of the box ∆
above the temperature of the outer surface. The total area of the box is , and the wall
thickness is .
a. Find the thermal conductivity of the material.
b. Calculate using 180 W, ∆ 61.0 , 2.43 m , and 4.40 cm.

Problem 17.15**
A carpenter builds a solid wood door with dimensions (height, width and thickness
respectively). The solid wood’s thermal conductivity is w . The air films on the inner and
outer surfaces of the door have the same combined thermal resistance as an additional add

3NBB0 ‐ Chapter 17 – Temperature and Heat 
Figures adapted from Young and Freedman, University Physics ed.12 
thickness of solid wood. The inside air temperature is in , and the outside air temperature
is out .
a. What is the rate of heat flow through the door?
b. A window of w w is inserted in the door. The glass has thickness glass , and has
thermal conductivity glass . The air films on the two sides of the glass have a total thermal
resistance that is the same as an additional add,glass of glass
By what factor is the heat flow increased?
c. Calculate the results of (a) and (b) using 2.10 m, 0.91 m, 6.0 cm,
54.0 cm, w 0.120 W/m ⋅ K, glass 0.80 W/m ⋅ K, add 1.9 cm, glass 0.50 cm,
add,glass 12 cm, in 21.0 , and out 5.0 .

Problem 17.16**
a. Compute the ratio of the rate of heat loss through a single-pane window with area to
that for a double-pane window with the same area. The glass of a single pane has
thickness , and the air (thermal conductivity ) space between the two panes of the
double-pane window is thick. The glass has thermal conductivity . The air films on
the room and outdoor surfaces of either window have a combined thermal resistance
of .
b. Calculate the result of (a) using 0.15 m , 4.5 mm, 0.024 W/m ⋅ K,
7.0 mm. 0.80 W/m ⋅ K, and 0.15 m ⋅ K/W.

Problem 17.17***
a. When the air temperature is below 0°C, the water at the surface of a lake freezes to form
an ice sheet. Why doesn’t freezing occur throughout the entire volume of the lake?
b. Show that the thickness of the ice sheet formed on the surface of a lake is proportional to
the square root of the time if the heat of fusion of the water freezing on the underside of
the ice sheet is conducted through the sheet.
c. Assuming that the upper surface of the ice sheet is at 10°C and the bottom surface is at
0 , calculate the time it will take to form an ice sheet 30 cm thick.
d. If the lake in part (c) is uniformly 50 m deep, how long would it take to freeze all the
water in the lake? Is this likely to occur?

Problem 17.18**
The icecaps of Greenland and Antarctica contain a fraction of the total water (by mass) on
the earth’s surface and the oceans contain a fraction . The rest (1 ) is mainly
groundwater.
a. Suppose the icecaps, currently at an average temperature of about ( 0), somehow
slid into the ocean and melted. What would be the resulting temperature decrease of the
ocean? Assume that the average temperature of ocean water is currently ( 0).

3NBB0 ‐ Chapter 17 – Temperature and Heat 
Figures adapted from Young and Freedman, University Physics ed.12 
b. Calculate the result of (a) using 0.0175, 0.975, 30 , and
5.00 .

Problem 17.19***
Consider a poor lost soul walking at 5 km/h on a hot day in the desert, wearing only a
bathing suit. This person’s skin temperature tends to rise due to four mechanisms: (i) energy
is generated by metabolic reactions in the body at a rate of 280 W, and almost all of this
energy is converted to heat that flows to the skin; (ii) heat is delivered to the skin by
convection from the outside air at a rate equal to skin air skin , where 54 J/h ⋅
⋅ m , the exposed skin area skin 1.5 m , the air temperature air 47 , and the skin
temperature skin 36 ; (iii) the skin absorbs radiant energy from the sun at a rate of
1400 W/m ; (iv) the skin absorbs radiant energy from the environment, which has
temperature 47 .
a. Calculate the net rate at which the person’s skin is heated by all four of these
mechanisms. Assume that the emissivity of the skin is 1.
Which mechanism is the most important?
b. At what rate must perspiration evaporate from this person’s skin to maintain a constant
skin temperature? (The heat of vaporization of water at skin 36 is 2.42
10 J/kg)
c. Suppose instead the person is protected by light-colored clothing ( 0) so that the
exposed skin area is only skin 0.45 m . What rate of perspiration is required now?
Discuss the usefulness of the traditional clothing worn by desert peoples.

Exercise 17.115

Problem 17.20***
A hollow cylinder has length , inner radius , and outer radius , and the temperatures at the
inner and outer surfaces are and . (The cylinder could represent an insulated hot-water
pipe.) The thermal conductivity of the material of which the cylinder is made is . Derive an
equation for
a. the total heat current through the walls of the cylinder;
b. the temperature variation inside the cylinder walls.
c. Show that the equation for the total heat current reduces to for linear heat
flow when the cylinder wall is very thin.
d. A steam pipe with a radius , carrying steam at , is
surrounded by a cylindrical jacket with inner and outer
radii and and made of a type of cork with thermal
conductivity . This in turn is surrounded by a
cylindrical jacket made of a brand of Styrofoam with
thermal conductivity and having inner and outer radii
and . The outer surface of the Styrofoam has a

3NBB0 ‐ Chapter 17 – Temperature and Heat 
Figures adapted from Young and Freedman, University Physics ed.12 
 temperature . What is the temperature at a radius , where the two insulating layers
meet?
e. What is the total rate of transfer of heat out of a piece of this pipe with length ?
f. Calculate the results of (d) and (e) using 2.00 cm, 4.00 cm, 6.00 cm,
140 , 4.00 10 W/m ⋅ K, 2.70 10 W/m ⋅ K, 15 , and
2.00 m.

3NBB0 ‐ Chapter 17 – Temperature and Heat 
Figures adapted from Young and Freedman, University Physics ed.12