Problem 25
The lowest air temperature recorded on Earth is \(-129^{\circ} \mathrm{F}\) in Antarctica. Convert this temperature to the Celsius scale.
Problem 27
A piece of dry ice (solid carbon dioxide) sitting in a classroom has a temperature of approximately \(-79^{\circ} \mathrm{C}\) a) What is this temperature in kelvins? b) What is this temperature in degrees Fahrenheit?
Problem 30
How does the density of copper that is just above its melting temperature of \(1356 \mathrm{~K}\) compare to that of copper at room temperature?
Problem 36
Even though steel has a relatively low linear expansion coefficient \(\left(\alpha_{\text {steel }}=13 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right),\) the expansion of steel railroad tracks can potentially create significant problems on very hot summer days. To accommodate for the thermal expansion, a gap is left between consecutive sections of the track. If each section is \(25.0 \mathrm{~m}\) long at \(20.0{ }^{\circ} \mathrm{C}\) and the gap between sections is \(10.0 \mathrm{~mm}\) wide, what is the highest temperature the tracks can take before the expansion creates compressive forces between sections?
Problem 37
A medical device used for handling tissue samples has two metal screws, one \(20.0 \mathrm{~cm}\) long and made from brass \(\left(\alpha_{\mathrm{b}}=18.9 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)\) and the other \(30.0 \mathrm{~cm}\) long and made from aluminum \(\left(\alpha_{\mathrm{a}}=23.0 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)\). A gap of \(1.00 \mathrm{~mm}\) exists between the ends of the screws at \(22.0^{\circ} \mathrm{C}\). At what temperature will the two screws touch?
Problem 38
You are designing a precision mercury thermometer based on the thermal expansion of mercury \(\left(\beta=1.8 \cdot 10^{-4}{ }^{\circ} \mathrm{C}^{-1}\right)\) which causes the mercury to expand up a thin capillary as the temperature increases. The equation for the change in volume of the mercury as a function of temperature is \(\Delta V=\beta V_{0} \Delta T\) where \(V_{0}\) is the initial volume of the mercury and \(\Delta V\) is the change in volume due to a change in temperature, \(\Delta T .\) In response to a temperature change of \(1.0^{\circ} \mathrm{C}\), the column of mercury in your precision thermometer should move a distance \(D=1.0 \mathrm{~cm}\) up a cylindrical capillary of radius \(r=0.10 \mathrm{~mm} .\) Determine the initial volume of mercury that allows this change. Then find the radius of a spherical bulb that contains this volume of mercury.
Problem 39
On a hot summer day, a cubical swimming pool is filled to within \(1.0 \mathrm{~cm}\) of the top with water at \(21{ }^{\circ} \mathrm{C} .\) When the water warms to \(37^{\circ} \mathrm{C}\), the pool overflows. What is the depth of the pool?
Problem 41
\(\cdot 17.41\) A clock based on a simple pendulum is situated outdoors in Anchorage, Alaska. The pendulum consists of a mass of 1.00 kg that is hanging from a thin brass rod that is \(2.000 \mathrm{~m}\) long. The clock is calibrated perfectly during a summer day with an average temperature of \(25.0^{\circ} \mathrm{C}\). During the winter, when the average temperature over one 24 -h period is \(-20.0^{\circ} \mathrm{C}\), find the time elapsed for that period according to the simple pendulum clock.
Problem 42
In a thermometer manufacturing plant, a type of mercury thermometer is built at room temperature \(\left(20^{\circ} \mathrm{C}\right)\) to measure temperatures in the \(20^{\circ} \mathrm{C}\) to \(70^{\circ} \mathrm{C}\) range, with \(\mathrm{a}\) \(1-\mathrm{cm}^{3}\) spherical reservoir at the bottom and a \(0.5-\mathrm{mm}\) inner diameter expansion tube. The wall thickness of the reservoir and tube is negligible, and the \(20^{\circ} \mathrm{C}\) mark is at the junction between the spherical reservoir and the tube. The tubes and reservoirs are made of fused silica, a transparent glass form of \(\mathrm{SiO}_{2}\) that has a very low linear expansion coefficient \((\alpha=\) \(\left.0.4 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right) .\) By mistake, the material used for one batch of thermometers was quartz, a transparent crystalline form of \(\mathrm{SiO}_{2}\) with a much higher linear expansion coefficient \(\left(\alpha=12.3 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right) .\) Will the manufacturer have to scrap the batch, or will the thermometers work fine, within the expected uncertainty of \(5 \%\) in reading the temperature? The volume expansion coefficient of mercury is \(\beta=181 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\).
Problem 46
Thermal expansion seems like a small effect, but it can engender tremendous, often damaging, forces. For example, steel has a linear expansion coefficient of \(\alpha=1.2 \cdot 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\) and a bulk modulus of \(B=160\) GPa. Calculate the pressure engendered in steel by a \(1.0^{\circ} \mathrm{C}\) temperature increase.
