Lawrence checked the air pressure in one of his tires before driving to school on a cold winter day. The tire pressure gauge registered 2.18 atmospheres (220.6 kPa). After making the 10 km trip to school, Lawrence checked the air pressure again. This time the gauge registered 2.31 atmospheres (234.4 kPa). Lawrence didn’t add any air to the tire in between the two measurements, so why did air pressure in the tire increase?
Keep on Rolling
There was no additional air in the tire the second time Lawrence checked the air pressure, but something did change between the two measurements. The tires had rolled over 10 km of road on the trip to school. Any time one surface moves over another, it causes friction. Friction is a force that opposes the motion of two surfaces that are touching, and friction between two surfaces always generates heat. Quickly rub your hands together and you’ll feel the heat generated by the friction between them. As the tires moved over the road, friction between the tires and road generated heat. In short, the tires got warmer and so did the air inside them.
It’s the Law!
The space inside a car tire is more-or-less fixed, so it has a constant volume. What happens when the volume of air is constant and its temperature increases? Lawrence found out the answer to that question when he measured the air pressure in his tire. Increasing the temperature of a gas such as air, while holding its volume constant, increases the pressure of the gas. This relationship between temperature and pressure of a gas is called Amontons' law. It was first proposed by a French scientist named Guillaume Amontons between 1700 and 1702. Because Amontons discovered the law beforehand, Gay-Lussac's name is now generally associated with the law of combining volumes of equal pressure and temperature. Amontons’ gas law is just one of three commonly known gas laws. The other two are Boyle’s law and Charles’ law.
Q: How does Amontons' gas law explain the difference in air pressure in Lawrence’s tire?
A: The tire—and the air inside it—got warmer because of friction with the road. The volume of air inside the tire was more-or-less constant, so the pressure of the air increased when it got warmer.
Why does the pressure of a gas increase as it gets warmer? Particles of a gas are constantly moving and bumping into things. The force of the collisions is measured by pressure. Pressure is the amount of force exerted on a given area, such as Newtons of force per square centimeter. When gas particles heat up and gain energy, they move faster. This causes more collisions and greater pressure. Therefore, heating particles of gas in a closed space causes the pressure of the gas to increase. Explore the behavior of gas particles at different temperatures in the model below. Change the temperature of the gas and watch what happens to its particles - and to the pressure.
Q: What happens to the pressure of the gas as its temperature increases?
A: The pressure of the gas increases as its temperature increases.
- According to Amontons’ law, increasing the temperature of a gas while holding its volume constant increases the pressure of the gas.
- When gas particles heat up and gain energy, they move faster. This increases their collisions with each other and their container, causing greater pressure.
- Amontons’ law: Gas law stating that, if the volume of a gas is held constant, increasing the temperature of the gas increases its pressure.
At normal air pressure, cans don't collapse. However, with some heat and some ice water, you can get a soda can to collapse at normal air pressure.
Watch the following simple demonstration, and then answer the questions below.
Now, use the model below to explore the molecular reason for why the can collapses.
The purple molecules (left side of the model) are in the can. The yellow molecules (right side of the model) are outside the can. The barrier between the molecules represents the wall of the can.
- Heating the Can: Simulate heating by pressing the "Heat" button for the purple molecules. The molecules in the can cannot evaporate out of the model, so you'll have to remove purple molecules from the inside of the can.
- Collapsing the Can: Simulate plunging the can into ice water by pressing the "Cool" button for the purple molecules several times.
- Try other combinations of heating, cooling and "Evaporation."
Q: In this model, when is the pressure of air inside the can greatest? Why?
Q: How is the volume of air inside the can kept constant after the can is heated and some molecules escape?
Q: What happens to the can wall when you rapidly cool the can in the model? Why?
- State Amontons’ law.
- Assume you have a sealed jug that contains only air. If you heat the air in the jug, it will have a higher temperature. What other property of the air will also change?
- A father does a classic experiment for his son, which is pictured in the Figure below. First, he put a small piece of paper in a glass bottle and lit the paper with a match. He immediately placed a shelled, hard-boiled egg over the bottle opening. The paper soon burned out, and after a few seconds, the egg slipped inside the bottle. Apply Amontons’ law to explain why.