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# Gas Pressure and Temperature Save Print Edit
Gas Pressure and Temperature
• Astrophysics • Atoms and Radioactivity • Electricity • Energy Physics • Engineering Physics • Fields in Physics • Force • Further Mechanics and Thermal Physics • Magnetism • Measurements • Mechanics and Materials • Medical Physics • Nuclear Physics • Particle Model of Matter • Physical Quantities and Units • Physics of Motion • Radiation • Space Physics • Turning Points in Physics • Waves Physics Why it is a bad idea to heat up a closed container of any kind of gas, including air? The reason is that it might build up pressure and the container could explode. This is caused by a direct relationship between the pressure and the temperature of the gas.

Heating up a gas leads to a higher pressure, so if the container gets really hot, it will not be able to withstand the immense pressure of the gas inside it anymore. It will explode! This article will explain the relationship between the pressure and the temperature of a gas.

## Meaning of gas pressure and temperature

We first need to know the meaning of the pressure and temperature of a gas. For this, we look at a gas as a bunch of particles flying around randomly inside a closed container of constant volume. See the animation below for the setup. Once in a while, the particles of the gas will hit the container wall and bounce back inwards, and this bounce exerts a force outwards on the container, perpendicular to the walls. This way, every unit area of the container experiences the same force from the bouncing gas particles.

The (perpendicular) force per unit area that bouncing gas particles exert on a wall is called the pressure of the gas.

We see that pressure is measured in units of , which we call pascal. The symbol of this unit is .

When we write out units in full, we always write them in all lower case, even if they are named after people. For example, the unit pascal is named after the physicist Pascal. Symbols of units can have capital letters, of which there are many examples, including .

If the particles in a gas exert a (perpendicular) force of on a area of a wall, then the pressure of that gas is .

The particles in a gas all have roughly the same speed (if they did not, bouncing off of each other would quickly result in a redistribution of the kinetic energy of the particles, and therefore distributed velocities), so there is a certain amount of average kinetic energy per gas particle. This energy per particle defines the temperature of the gas: the faster the particles move, the higher the temperature of the gas. A gas of particles in a container, Wikimedia Commons

## Relationship between gas pressure and temperature

From the definitions and the setup of the gas in a closed container, we see that an increase in gas temperature, and therefore an increase in the average speed of the gas particles, will lead to more frequent (if the volume of the closed gas container remains constant) and more violent bounces against the walls of the container. In other words, heating up a gas in a container of constant volume increases the number of collisions between particles and the walls of the container, and it increases the average force of the collisions with the container. This means that the total force per unit area of the container walls increases, which, by definition, means that this increases the pressure of the gas.

We can also visualise this increase in pressure using the animation above. If the speed of the particles increases, then we intuitively see that the particles exert a larger force on the container walls. Thus, the relationship between the temperature and the pressure of a gas - given a constant container volume - is positive: an increase in gas temperature means an increase in gas pressure. Inversely, given a constant container volume, an increase in gas pressure means an increase in gas temperature, because the only way for the pressure to increase is for the particles to move faster, which means that the temperature increases.

For a closed container of constant volume (i.e. a constant volume and a constant number of particles in the gas), the gas pressure is a constant multiplied by the temperature. In other words, the relationship between gas pressure and temperature is linear. In practice, this means the following.

If, in a closed container of constant volume, the temperature doubles, then the pressure also doubles. If the temperature drops, then the pressure also drops, by the same factor.

## Gas pressure and temperature graph

As the relationship between gas pressure and temperature is positive, the pressure-temperature graph corresponding to a gas consists of an increasing curve. As it turns out, the graph will actually be a straight line (because of the linearity we mentioned in the deep dive above), but you do not need to know this. Below, we see the graph corresponding to a typical gas you may find on Earth. Graph of the pressure as a function of the temperature of a typical gas - StudySmarter Originals

We see that around the freezing point of water , the pressure of this gas is approximately . In practice, this is the pressure of the air around us: atmospheric pressure is approximately . We also see that at a temperature of , the pressure is : this is logical because particles don't move at a temperature of absolute zero, so they don't bounce off of any walls either.

## Gas pressure and temperature experiments

Take any empty closed container of constant volume and heat it up, for example by using fire. The temperature of the air inside the container will rise, so the pressure of the air will increase as well. At some air temperature, the force that the air exerts on the container through its pressure becomes too big for the container to stay in one piece: the container explodes. Obviously, this experiment is dangerous to perform in practice, but it is a nice and simple thought experiment. Air receiver burst due to too much internal pressure, Wikimedia Commons Public Domain.

This is an experiment you can do at home. Take a plastic water (or soft drink) bottle, empty it such that mainly air is inside, and close it off with the cap. Now put the bottle in your freezer and wait for about 5 minutes. The bottle probably has dents in it. These are caused by the decrease in pressure of the air inside the bottle because of the cooling! Taking the bottle out of the freezer will warm the air inside it up again, and the bottle will un-dent itself in front of you. This un-denting visualises the increase in air pressure inside the bottle, which is a direct result of the reheating of that air.

## Examples of using the gas pressure-temperature relationship

Suppose we have an empty closed container of constant volume: it only contains air, and this air has a certain pressure

If we heat up the container, the air will be heated as well, so the pressure of the air inside the container will increase. On the other hand, if we put the container in the freezer, the gas temperature will decrease, so the gas pressure will decrease.

If we cannot measure the temperature of the container directly, but we are able to measure the pressure of the air inside the container, we can still say things about the temperature of the air in the container. Namely, if the pressure is increasing, we know that the temperature must be increasing, and if the pressure is decreasing, we know that the temperature must be decreasing.

## Gas Pressure and Temperature - Key takeaways

• When thinking about gases, visualise particles flying around randomly. If there is a wall, they bounce off it, and this bouncing exerts a force on the wall.
• The pressure of a gas is the force per unit area that it would exert on a (potentially purely hypothetical) wall.
• The temperature of a gas is dictated only by the average energy of the particles in the gas.
• For a gas in a closed container of constant volume, an increase in temperature always goes together with an increase in pressure, and vice versa.
• The graph of pressure versus temperature is an increasing line.
• Heating up a closed container of constant volume will make the gas pressure increase, which will at some point make the container explode.
• We can say things about the temperature of a gas by measuring its pressure, and vice versa.

Temperature affects gas pressure as follows: for an ideal gas in a constant volume and particle number, the pressure is linear in temperature. This means that a percentage change in temperature causes the same percentage change in pressure.

Temperature changes with pressure as follows: for an ideal gas in a constant volume and particle number, the temperature is linear in pressure. This means that a percentage change in pressure causes the same percentage change in temperature.

Causes of gas pressure and temperature changes can be a change in the particle density of the gas (either by shrinking its volume or by adding particles), or manual heating of the gas.

An increase in temperature of a gas will either lower its density (if the pressure is being held constant, e.g. in the atmosphere), or increase its pressure (if its density is being held constant, e.g. in a closed container).

The equation/formula for calculating gas pressure from temperature and vice versa is the ideal gas law: pV=NkT. If you know the particle density of a gas, you have a direct (linear) relationship between gas pressure and temperature.

## Final Gas Pressure and Temperature Quiz

Question

Describe the model for a gas.

A gas can be viewed as a bunch of particles flying around randomly, bumping into each other and into walls. The particles all have roughly the same speed.

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Question

What is the pressure of a gas?

The pressure of a gas is the force per unit area that it would exert on a wall.

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Question

Is the temperature of a gas dictated ONLY by the energy of the particles in the gas?

Yes

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Question

Describe what it means for the relationship between gas pressure and temperature to be positive.

For example, this means that an increase in temperature implies an increase in pressure, and a decrease in pressure implies a decrease in temperature.

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Question

Describe the graph of pressure versus temperature of a gas.

The graph is an increasing line.

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Question

What is the pressure of a gas at a temperature of absolute zero?

Around 0 Pa

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Question

Describe a demonstration of the relationship between pressure and temperature.

- Heating up an empty closed container will increase the air pressure inside. At some point, the container explodes.
- Putting an empty water bottle in the freezer, which causes the bottle to dent.

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Question

Explain according to the particle model of a gas how an increase in temperature causes an increase in pressure.

An increase in temperature means higher speeds of the particles. This means more frequent and more forceful collisions with a (hypothetical) container wall, which are 2 factors that increase the pressure of the gas.

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Question

We close an open container at atmospheric pressure and room temperature and start heating it up. What can we say about the pressure of the gas?

It increases

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Question

What is one Pa expressed in N and m?

N/m2

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Question

In a closed container containing a gas, what does a doubling of the pressure mean for its temperature?

The temperature increases

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Question

If you have an empty water bottle and a freezer at hand, how would you make the water bottle bulge using what you know about pressure and temperature?

You would put the water bottle in the freezer with the cap off, wait a few minutes, screw the cap on, and take the bottle out. The heating of the air inside the bottle will cause the pressure to increase, making the bottle bulge.

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Question

If a closed container implodes, what can you say about what happened to the temperature of the gas inside it?

It decreased.

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Question

Does a gas that is not surrounded by walls have a pressure?

Yes, we can always insert hypothetical walls to see what force would be on it, and we define pressure that way.

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Question

Can a gas have a negative pressure?

No, because particles always push against walls, they can't pull on them.

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