1.3 Thermal Expansion

Does a given reading on a gasoline gauge indicate more gasoline in cold weather or in hot weather, or does the temperature not matter?

Two objects A and B have the same dimensions and are constrained identically. A is made of a material with a higher thermal expansion coefficient than B. If the objects are heated identically, will A feel a greater stress than B?

Pouring cold water into hot glass or ceramic cookware can easily break it. What causes the breaking? Explain why Pyrex®, a glass with a small coefficient of linear expansion, is less susceptible.

Does it really help to run hot water over a tight metal lid on a glass jar before trying to open it? Explain your answer.

Calculate the length of a 1-meter rod of a material with thermal expansion coefficient $\alpha$ when the temperature is raised from 300 K to 600 K. Taking your answer as the new initial length, find the length after the rod is cooled back down to 300 K. Is your answer 1 meter? Should it be? How can you account for the result you got?

The height of the Washington Monument is measured to be 170.00 m on a day when the temperature is $35.0 ° \text{C}.$ What will its height be on a day when the temperature falls to $−10.0 ° \text{C}$? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.

What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from $37.0 ° \text{C}$ to $40.0 ° \text{C}$, assuming the mercury is constrained to a cylinder but unconstrained in length? Your answer will show why thermometers contain bulbs at the bottom instead of simple columns of liquid.

You are looking to buy a small piece of land in Hong Kong. The price is “only” $60,000 per square meter. The land title says the dimensions are $20 \text{m} \times 30 \text{m}$. 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 $20 ° \text{C}$ above the temperature that the tape measure was designed for? The dimensions of the land do not change.

(a) Suppose a meter stick made of steel and one made of aluminum are the same length at $0^{} ° \text{C}$. What is their difference in length at $22.0 ° \text{C}$? (b) Repeat the calculation for two 30.0-m-long surveyor’s tapes.

Most cars have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 16.0-L capacity when at $10.0 ° \text{C}$. What volume of radiator fluid will overflow when the radiator and fluid reach a temperature of $95.0 ° \text{C},$ given that the fluid’s volume coefficient of expansion is $\beta = 400 \times 10^{−6} / ° \text{C}$? (Your answer will be a conservative estimate, as most car radiat…

The density of water at $0 ° \text{C}$ is very nearly $1000 \text{kg}/\text{m}^{3}$ (it is actually $999.84 \text{kg}/\text{m}^{3}$), whereas the density of ice at $0 ° \text{C}$ is $917 \text{kg}/\text{m}^{3} .$ Calculate the pressure necessary to keep ice from expanding when it freezes, neglecting the effect such a large pressure would have on the freezing temperature. (This problem gives you only an indication of how large the forces associated with freezing water might be.)