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Solved problems for the chapter:

Area and Volume Expansivities

View the theory »

Thermal Expansion

1. Linear expansion

2. Cubic expansion

3. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:area_and_volume_expansivities/5115/

Example 1.

At a temperature of 5 °C, we have 4.97 litres of oil in a 5.00-litre container. When the ambient temperature is slowly increased to 85 °C, the volume of the container increases by 0.02 litre, and 2 % of oil is spilled over the edge of the containe. What is the cubic expansivity of the container and oil?

Example 2.

An aluminium wire is used to form a rectangle of side length and width at 20 °C. The rectangle is then heated to 70 °C. Calculate the ratio of the:

diagonals
perimeters
areas

of the rectangle at the initial temperature (20 °C ) to that at the final temperature (70 °C), correct to 4 decimal places.

The linear expansivity of aluminium is .

A spherical iron ball has a radius of and density at . It is then placed in a furnace at . If the mass of the ball remains the same, what is the density of the ball at ? The linear expansivity of iron is .

At 20 °C, the diameter of a plug is 8.753 cm and the inner diameter of a ring is 8.743 cm. At what temperature would the plug go into the ring in the following cases?

the plug is brass and inserted into an iron ring.
the plug is made of iron and the ring is made of brass.

Th linear expansivity of iron is and that of brass is .

From a flask containing air, a thin tube leads into a container of water.

The flask is heated with a burner. What happens to the contents of the flask?
The flask is then cooled with ice. What happens to the contents of the flask?

a) heating the flask b) cooling the flask

A mercury thermometer consists of a glass flask with a volume of and a capillary tube. What must be the inner radius of the capillary tube for a change in temperature to correspond to a 1 mm change in mercury length? The difference between the cubic expansivity of mercury and glass is .

The circumference of a copper ring at a temperature of 20 °C is equal to 2.000 m. To what temperature do we need to heat the ring to increase the area of the circle bounded by the ring by 2 % of the original area?

The linear expansivity of copper is .

For most materials, when the temperature increases, they expand and their density decreases, and when the temperature decreases, they contract, and their density increases. This rule does not apply to water. Answer the following questions:

At what temperature is water densest?
Why does ice float on water?
What is the temperature of the water at the bottom of Lake Bled during winter when there is a layer of ice on top?
How is it that the fish in the lake do not freeze in the winter when children are already skating on the lake?

The table below shows the linear expansivities of steel and glass. Explain why it is easier to unscrew the steel lid on a glass jar of pickled fruit when you immerse the whole jar in warm water.

10.

What is the percent increase in the area of a copper plate if its temperature is increased by 300 K? The linear expansivity of copper is .

11.

A square-shaped plate is heated. The length of each side of the square increases by after heating. By what percentage does the area of the plate increase?

12.

What is the density of mercury at if its density at is equal to . The cubic expansivity of mercury is .

13.

The temperature of an iron cube is increased by 500 K.

What is the percent increase in its volume?
What is the percent increase in the length of its edge?

The linear expansivity of iron is .

14.

What is the percentage change in the volume of a cube whose edge is stretched by of its original length?