# Worksheet: Thermal Expansion of Solids and Liquids

In this worksheet, we will practice relating the linear and volume expansion coefficients of solids and liquids to objects' size changes with temperature.

**Q2: **

You are looking to buy a small piece of land in Hong Kong. The price is “only” per square meter. The land title says the dimensions are 20 m by 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 above the temperature that the tape measure was designed for? The dimensions of the land do not change. The coefficient of thermal expansion of steel is .

**Q3: **

A volume of mercury is contained in a tall, thin, cylinder. The mercury fills the cylinder to a height of 3.0 cm and is at a temperature of . If the mercury is heated to a temperature of , how much does the height of the column of mercury increase? Use a value of for the linear coefficient of expansion of mercury.

- A m
- B m
- C m
- D m
- E m

**Q4: **

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 . What volume of radiator fluid will overflow when the radiator and fluid reach a temperature of given that the fluid’s volume coefficient of expansion is and copper’s volume coefficient of expansion is ?

**Q5: **

Find the stress exerted on a steel beam along its length if the beam has no lengthwise space to expand into and its temperature increases from to . Use a value of for the Young’s modulus of steel and use a value of for the coefficient of thermal expansion of steel. Ignore any change in the cross-sectional area of the beam due to heating.

- A Pa
- B Pa
- C Pa
- D Pa
- E Pa

**Q6: **

A 1.0-m-long stick made of steel and a 1.0-m-long stick made of aluminium are the same length as each other when they are both at a temperature of . Both sticks expand when heated. Use a value of for the coefficient of thermal expansion of steel and use a value of for the coefficient of thermal expansion of aluminium.

What is the difference in length of the two sticks when both are at a temperature of ?

- A m
- B m
- C
- D m
- E

A steel tape and an aluminium tape are both 30.0 m in length at a temperature of . What is the difference in length of the tapes when both are at a temperature of ?

- A m
- B
- C m
- D m
- E

**Q7: **

A glass beaker has a capacity of 397 mL. The beaker is filled to the brim with water that is at a temperature of . Determine the volume of water that will overflow the beaker when the water’s temperature increases to . Use a value of for the coefficient of volumetric expansion of water.

**Q8: **

An engineer wants to design a structure in which the difference in length between a steel beam and an aluminium beam remains at 0.730 m when they both vary in temperature by the same amount. In determining the relationship between the lengths of the beams, use a value of for the linear thermal expansion coefficient of aluminium and for the linear thermal expansion coefficient of steel.

What must the length of the steel beam be?

- A 1.35 m
- B 0.672 m
- C 0.337 m
- D 1.40 m
- E 0.700 m

What must the length of the aluminium beam be?

- A 0.672 m
- B 0.337 m
- C 1.35 m
- D 1.40 m
- E 0.700 m

**Q9: **

An aluminium pendulum used to drive a grandfather clock has a length m and a mass at temperature . The clock can be modeled as a physical pendulum consisting of a rod oscillating around one of its ends. Determine the percent increase in the period of the clock if the temperature increases by , assuming the length of the rod changes linearly with temperature, where . Use a value of for , the linear temperature coefficient of expansion of aluminium.

- A
- B
- C
- D
- E

**Q10: **

A farmer making grape juice fills a glass bottle to the brim and caps it tightly. After capping, the juice and bottle warm up and expand. The juice’s thermal expansion is greater than the glass’s thermal expansion. The juice’s volume increases more than the bottle’s volume increases. Take the bulk modulus of the juice to be N/m^{2} and calculate the force exerted per square centimeter by the juice on the bottle.

- A N/cm
- B N/cm
- C N/cm
- D N/cm
- E N/cm

**Q11: **

A brass rod that is at a temperature of has a length of 1.12 m and a diameter of 0.6700 cm. The rod is fixed at both of its ends and then its temperature is increased, creating a compressive force along the length of the rod. Determine the temperature at which the rod will be subject to a force of 28.0 kN. Use a value of Pa for the Young’s modulus of brass and use a value of for the linear thermal expansion coefficient of brass. Assume that any change in the radius of the rod due to thermal expansion is negligible.

**Q12: **

A physicist makes
cm^{3}
of instant coffee, which he pours into a cup that has
a radius of 10.00 cm.
As the coffee cools from a temperature of
to ,
the physicist notices that the vertical
height of the column of coffee decreases by 4.50 mm.
Determine what percent of the decrease of the height of
the column of coffee is due to the thermal contraction of the coffee.
Use a value of
for the coefficient of volumetric expansion of the coffee.

- A
- B
- C
- D
- E

**Q13: **

Determine how large of an expansion gap should be left between steel railway rails if they may reach a maximum temperature of greater than when they were laid down. The original length of the rails is 8.0 m. Use a value of for the coefficient of linear expansion of steel.

- A 9.2 mm
- B 2.3 mm
- C 1.2 mm
- D 4.6 mm
- E 5.0 mm

**Q14: **

Determine how much taller the Eiffel Tower becomes at the end of a day when the temperature has increased by . Use a value of 312.0 m as the original height of the tower and for the coefficient of linear expansion of steel.

**Q15: **

Global warming will produce rising sea levels partly due to melting ice caps and partly due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, determine the change in length of a column of water 3.50 km high for a temperature increase of . Assume the column is not free to expand sideways and neglect the variation of ocean water warming with depth. Use a value of for the coefficient of linear expansion of water.