Section 9 - Sample problem: thermal expansion and stress
9.1 A copper rod at a temperature of 22.82°C is bolted in place between two rigid walls. What stress does the rod exert (the force
on each of the perfectly rigid walls, divided by the area of contact) when it is heated to a temperature of 274.2°C? (The
coefficient of linear expansion for copper is 1.65×10í^5 1/C°, and Young's modulus for the material is 1.08×10^11 N/m^2 .)
N/m^2
9.2 A rod has a cross-sectional area of 0.001615 m^2. When the rod's temperature is 12.23°C, it is placed between two rigid walls
that are exactly as far apart as the length of the rod. The rod's temperature then increases to 27.23°C, and the rod exerts a
force of 5.334×10^4 N on each wall. If Young's modulus for the material of which the rod is made is 1.05×10^11 N/m^2 , what is the
coefficient of linear expansion of the rod?
1/C °Section 11 - Thermal expansion: volume
11.1 A lead ball has a volume of 94.3 cm^3 at 19.3°C. What is the change in volume when its temperature changes to 32.3°C?
cm^311.2 A solid copper ball with radius 1.35 cm increases in temperature from 15°C to 86°C. What is the change in its volume?
cm^311.3 A hot water tank holds exactly 80.0 gallons of water at 115°F. What is the volume of the water at 40.0°F?
gallons11.4 The density of mercury at 0°C is 13,595 kg/m^3. What is its density at
100.0°C?
kg/m^3
11.5 Fever thermometers are often made of a glass tube filled with a liquid. Older thermometers were often filled with mercury.
Newer ones are filled with red-tinted ethyl alcohol. You have two identical glass tube thermometers, one filled with mercury
and the other filled with ethyl alcohol. The degree marks on the mercury thermometer are 1.32×10í^3 m apart. How far apart
are they on the alcohol thermometer? (Ignore the expansion of the glass in your calculations. The coefficient of volume
expansion is 1.12×10í^3 1/C° for ethyl alcohol.)
m
11.6 A cup is made from a thin sheet of aluminum, shaped into a cylinder open at one end. At 13.4°C, the radius of the cylinder is
3.24 cm and its height is 7.56 cm. (a) What is the change in volume of the cup when it is raised to a temperature of 78.2°C?
(The coefficient of linear expansion for aluminum is 2.31×10í^5 1/C°.) (b) If the cup is initially exactly filled to the brim with
water, and the water is raised to the same temperature as the cup, what volume of water bulges out over the top of the cup?
(The coefficient of volume expansion for water is 20.7×10í^5 1/C°.)
(a) cm^3
(b) cm^3
11.7 The temperature of a block of lead is raised from 0°C to 100°C. What is the percentage change in its density? (The density
of lead at 0°C is 11,300 kg/m^3 .)
%Section 12 - Specific heat
12.1 A block of iron at 35.0°C has mass 2.30 kg. If 3.50×10^4 J of heat are transferred to the block, what is its resulting
temperature?
°C12.2 You want to take a bath with the water temperature at 35.0°C. The water temperature is 38.0°C from the hot water tap and
11.0°C from the cold water tap. You fill the tub with a total of 191 kg of water. How many kilograms of water from the hot
water tap do you use?
kg
12.3 An orchid grower hears that the temperature is expected to fall below freezing overnight, so she puts a large barrel in her
orchid greenhouse and fills it with 315 kg of water at 21.0°C. In the morning, the water is at 1.5°C. How much heat left the
water during the night? (Express the answer as a positive amount.)
J