Chapter 17

At room temperature, an iron horseshoe, when dunked into a cylindrical tank of water (radius of \(10.0 \mathrm{~cm})\) causes the water level to rise \(0.25 \mathrm{~cm}\) above the level without the horseshoe in the tank. When heated in the blacksmith's stove from room temperature to a temperature of \(7.00 \cdot 10^{2} \mathrm{~K}\) worked into its final shape, and then dunked back into the water, how much does the water level rise above the "no horseshoe" level (ignore any water that evaporates as the horseshoe enters the water)? Note: The linear expansion coefficient for iron is roughly that of steel: \(11 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\).

The volume of \(1.00 \mathrm{~kg}\) of liquid water over the temperature range from \(0.00^{\circ} \mathrm{C}\) to \(50.0^{\circ} \mathrm{C}\) fits reasonably well to the polynomial function \(V=1.00016-\left(4.52 \cdot 10^{-5}\right) T+\) \(\left(5.68 \cdot 10^{-6}\right) T^{2}\), where the volume is measured in cubic meters and \(T\) is the temperature in degrees Celsius. a) Use this information to calculate the volume expansion coefficient for liquid water as a function of temperature. b) Evaluate your expression at \(20.0^{\circ} \mathrm{C}\), and compare the value to that listed in Table \(17.3 .\)

a) Suppose a bimetallic strip is constructed of copper and steel strips of thickness \(1.0 \mathrm{~mm}\) and length \(25 \mathrm{~mm},\) and the temperature of the strip is reduced by \(5.0 \mathrm{~K}\). Determine the radius of curvature of the cooled strip (the radius of curvature of the interface between the two strips). b) If the strip is \(25 \mathrm{~mm}\) long, how far is the maximum deviation of the strip from the straight orientation?

A copper cube of side length \(40 . \mathrm{cm}\) is heated from \(20 .{ }^{\circ} \mathrm{C}\) to \(120{ }^{\circ} \mathrm{C}\). What is the change in the volume of the cube? The linear expansion coefficient of copper is \(17 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\).

When a 50.0 -m-long metal pipe is heated from \(10.0^{\circ} \mathrm{C}\) to \(40.0^{\circ} \mathrm{C}\), it lengthens by \(2.85 \mathrm{~cm}\). a) Determine the linear expansion coefficient. b) What type of metal is the pipe made of?

On a cool morning, with the temperature at \(15.0^{\circ} \mathrm{C}\), a painter fills a 5.00 -gal aluminum container to the brim with turpentine. When the temperature reaches \(27.0^{\circ} \mathrm{C}\), how much fluid spills out of the container? The volume expansion coefficient for this brand of turpentine is \(9.00 \cdot 10^{-4}{ }^{\circ} \mathrm{C}^{-1}\).

In order to create a tight fit between two metal parts, machinists sometimes make the interior part larger than the hole into which it will fit and then either cool the interior part or heat the exterior part until they fogether. Suppose an aluminum rod with diameter \(D_{1}\) (at \(\left.2.0 \cdot 10^{1}{ }^{\circ} \mathrm{C}\right)\) is to be fit into a hole in a brass plate that has a diameter \(D_{2}=10.000 \mathrm{~mm}\) (at \(\left.2.0 \cdot 10^{1}{ }^{\circ} \mathrm{C}\right) .\) The machinists can cool the rod to \(77.0 \mathrm{~K}\) by immersing it in liquid nitrogen. What is the largest possible diameter that the rod can have at \(2.0 \cdot 10^{1}{ }^{\circ} \mathrm{C}\) and just fit into the hole if the rod is cooled to \(77.0 \mathrm{~K}\) and the brass plate is left at \(2.0 \cdot 10^{1}{ }^{\circ} \mathrm{C} ?\) The linear expansion coefficients for aluminum and brass are \(22 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\) and \(19 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\), respectively.

An aluminum vessel with a volume capacity of \(500 . \mathrm{cm}^{3}\) is filled with water to the brim at \(20 .{ }^{\circ} \mathrm{C} .\) The vessel and contents are heated to \(50 .{ }^{\circ} \mathrm{C} .\) During the heating process, will the water spill over the top, will there be more room for water to be added, or will the water level remain the same? Calculate the volume of water that will spill over or that could be added if either is the case.

A plastic-epoxy sheet has uniform holes of radius \(1.99 \mathrm{~cm}\). The holes are intended to allow solid ball bear- ings with an outer radius of \(2.00 \mathrm{~cm}\) to just go through. Over what temperature rise must the plastic-epoxy sheet be heated so that the ball bearings will go through the holes? The linear expansion coefficient of plastic-epoxy is about \(1.3 \cdot 10^{-4}{ }^{\circ} \mathrm{C}^{-1}\).

A 25.01 -mm-diameter brass ball sits at room temperature on a 25.00 - mm- diameter hole made in an aluminum plate. The ball and plate are heated uniformly in a furnace, so both are at the same temperature at all times. At what temperature will the ball fall through the plate?