# Worksheet: Thermal Expansion of Solids and Liquids

In this worksheet, we will practice calculating the linear and volumetric expansion of solids and liquids due to their change in temperature.

**Q1: **

A solid rod is made of a substance that has a linear coefficient of thermal expansion of . The rod increases in length by 0.12 mm when its temperature increases by . Find the length of the rod after this temperature increase. Answer to three significant figures.

**Q2: **

Water in a tank is increased in temperature from to . The water volume increases by 0.25 L. Find the volume of the water before the temperature increase. Use a value of for the volume coefficient of expansion of water. Answer to three significant figures.

**Q3: **

Two wires increase in length by the same amount when both their temperatures increase by the same amount, as shown in the diagram. Before the temperature increase, the longer wire is 1.2525 m long. The shorter wire’s linear coefficient of thermal expansion is 1.135 times that of the longer wire. How much shorter is the shorter wire before the temperature increase? Answer to three significant figures.

**Q4: **

A 10 cm long thread of a substance is at a temperature of . The substance has a linear thermal expansion coefficient of . Find the minimum possible length of the thread. Give your answer to three significant figures.

**Q5: **

A thin strip of an unknown substance expands in length from 12.5 cm to 12.8 cm, as shown in the diagram. The temperature change of the strip is . Find the linear thermal expansion coefficient of the substance. Answer to three significant figures.

- A
- B
- C
- D
- E

**Q6: **

A thin strip of copper with a linear thermal expansion coefficient of increases its length by 0.25%. How much does the strip’s temperature increase by? Answer to three significant figures.

**Q7: **

A 250 L volume of water is increased in temperature from to . Find the increase in the volume of the water. Use a value of for the volume coefficient of expansion of water. Answer to three significant figures.

**Q8: **

A 65 cm length of wire is increased in temperature by . The wire has a linear thermal expansion coefficient of . Find the change in the length of the wire. Answer to three significant figures.

**Q9: **

A cube of an unknown material has a mass of 1.382 kg. The
cube is heated by 50.53 kJ and its volume increases from
0.01252 m^{3}
to 0.01275 m^{3}.

Determine the ratio of the object’s specific heat capacity in joules per kilogram degree Celsius to its volume coefficient of thermal expansion in reciprocal degrees Celsius (). Answer to three significant figures.

Which of the following is a valid unit for the ratio of the specific heat capacity to the volume coefficient of thermal expansion?

- A J/kg
- B
- C
- D J⋅kg