13.2 Thermal Expansion of Solids and Liquids

The height of the Washington Monument is measured to be 170 m on a day when the temperature is $\text{35} . 0 º \text{C}$. What will its height be on a day when the temperature falls to $– \text{10} . 0 º \text{C}$? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble’s.

What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from $\text{37} . 0 º \text{C}$ to $\text{40} . 0 º \text{C}$, assuming the mercury is unconstrained?

You are looking to purchase a small piece of land in Hong Kong. The price is “only” $60,000 per square meter! The land title says the dimensions are $\text{20} \text{ m } \times \text{30 m} .$ By how much would the total price change if you measured the parcel with a steel tape measure on a day when the temperature was $\text{20} º \text{C}$ above normal?

Show that 60.0 L of gasoline originally at $\text{15} . 0 º \text{C}$ will expand to 61.1 L when it warms to $\text{35} . 0 º \text{C},$ as claimed in the example.

(a) If a 500-mL glass beaker is filled to the brim with ethyl alcohol at a temperature of $5 . \text{00} º \text{C},$ how much will overflow when its temperature reaches $\text{22} . 0 º \text{C}$? (b) How much less water would overflow under the same conditions?

A physicist makes a cup of instant coffee and notices that, as the coffee cools, its level drops 3.00 mm in the glass cup. Show that this decrease cannot be due to thermal contraction by calculating the decrease in level if the $\text{350} \text{ cm}^{3}$ of coffee is in a 7.00-cm-diameter cup and decreases in temperature from $\text{95} . 0 º \text{C}$to$\text{45} . 0 º \text{C} .$ (Most of the drop in level is actually due to escaping bubbles of air.)

Show that $\beta \approx 3α ,$ by calculating the change in volume $\Delta V$ of a cube with sides of length $L .$