20. Heat and Temperature

An aluminum rod is exactly $80.00\mathrm{cm}$ long on a day when the temperature was $24.00°\mathrm{C}$. How long is the rod on a day when it is only $2.000°\mathrm{C}$? Use $2.3\times {10}^{-5}°{\mathrm{C}}^{-1}$ for the coefficient of linear expansion for aluminum.

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?

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

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?

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?

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?

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?