20. Heat and Temperature

Linear Thermal Expansion

Multiple Choice
On a very cold day at a temperature of –12°C, a power line made of aluminum between two support towers measures exactly 150.56m. You go out on a hot day and measure the power line to be exactly 150.71m. What is the temperature (in °C) outside? The linear expansion coefficient of aluminum is 2.4×10^-5.
Multiple Choice
An aluminum rod is exactly $80.00 cm$ long on a day when the temperature was $24.00 ° C$ . How long is the rod on a day when it is only $2.000 ° C$ ? Use $2.3 \times 10^{- 5} ° C^{- 1}$ for the coefficient of linear expansion for aluminum.
Open Question
Steel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -9.0°C. (a) How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 33.0°C?
Open Question
As a new mechanical engineer for Engines Inc., you have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0°C and 150.0°C. Assume that the coefficients of expansion are constant over this temperature range. (a) If the piston just fits inside the chamber at 20.0°C, will the engines be able to run at higher temperatures? Explain
Open Question
One of the tallest buildings in the world is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15.5°C. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that the Taipei 101 is 0.471 foot taller than its official height. What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel?
Open Question
The 828-m-tall Burj Khalifa in Dubai is the world's tallest building. It's essentially a steel building wrapped in exterior paneling and glass. During construction, when the beams were exposed to the elements, the building was 36 cm taller on the hottest afternoon of the year than on the coldest morning. By how much did the temperature vary throughout the year?
Open Question
At room temperature (20°C), a 5.0-cm-long brass rod is 20 μm too long to fit into a slot. To what temperature should you cool the rod so that it just barely fits?
Open Question
A surveyor has a steel measuring tape that is calibrated to be 100.000 m long (i.e., accurate to ±1 mm) at 20°C. If she measures the distance between two stakes to be 65.175 m on a 3°C day, does she need to add or subtract a correction factor to get the true distance? How large, in mm, is the correction factor?
Open Question
(I) A concrete highway is built of slabs 14 m long at 15°C. How wide should the expansion cracks between the slabs be (at 15°C) to prevent buckling if the range of temperature is - 30° C to + 50° C?
Open Question
(II) To what temperature would you have to heat a brass rod for it to be 1.5% longer than it is at 22°C?
Open Question
(II) A brass plug is to be placed in a ring made of iron. At 15°C, the diameter of the plug is 8.756 cm and that of the inside of the ring is 8.742 cm. They must both be brought to what common temperature in order to fit?
Open Question
(a) A horizontal steel I-beam of a cross-sectional area of 0.041 m² is rigidly connected to two fixed vertical supports. If the beam was installed when the temperature was 25°C

(b) Is the ultimate strength of the steel exceeded?

(c) What stress is developed if the concrete beam has a cross-sectional area of 0.15m²? Will it fracture?
Open Question
(I) The Eiffel Tower (Fig. 17–20) is built of wrought iron approximately 300 m tall. Estimate how much its height changes between January (average temperature of 2°C) and July (average temperature of 25°C). Ignore the angles of the iron beams and treat the tower as a vertical beam.
<IMAGE>
Open Question
If a steel band were to fit snugly around the Earth’s equator at 25°C but then was heated to 55°C, how high above the Earth would the band be (assume equal everywhere)?
Open Question
A precise steel tape measure has been calibrated at 14°C. At 37°C,
(b) what will be the percentage error?