# Gas Pressure and Temperature

Have you ever wondered why it's dangerous to heat up a closed container of gas, like air? The answer is simple. As you heat up the gas, the pressure inside the container increases. If the temperature gets too high, the container won't be able to handle the pressure and it could explode! This all happens because there's a direct link between the temperature and pressure of gas. Let's explore this relationship between gas pressure and temperature more in this article.

## Meaning of gas pressure and temperature

To understand gas pressure and temperature, let's imagine a closed container with gas particles flying around inside. Sometimes, these particles hit the walls of the container and bounce back inwards, creating a force outward on the container. This force per unit area is called gas pressure, measured in pascal (symbol: Pa). Gas particles also have average kinetic energy, which determines the temperature of the gas. The faster the particles move, the higher the temperature. Remember, units are always written in lowercase, even if named after a person, like pascal.

## 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

The pressure-temperature graph of a gas is typically an increasing curve due to the positive relationship between gas pressure and temperature. However, as we mentioned earlier, the relationship between gas pressure and temperature is linear, so the graph is actually a straight line. The slope of this line depends on the gas and its properties, such as the number of particles, and their masses and speeds. Below is a typical pressure-temperature graph of a gas found on Earth.

We can see from the pressure-temperature graph that at the freezing point of water, the pressure of the gas is approximately equal to atmospheric pressure, which is around 101.3 kPa or 1 atm. At a temperature of absolute zero (-273.15°C), the pressure of the gas is zero because the particles are not moving and hence not colliding with the walls of the container. This makes sense because at absolute zero, all molecular motion ceases, and the gas would be in its lowest possible energy state.

## Gas pressure and temperature experiments

You are correct. Heating up a closed container of constant volume will cause the temperature of the air inside the container to increase, leading to an increase in the pressure of the air. This is because the gas molecules inside the container will have higher kinetic energies and will collide more frequently with the walls of the container, exerting a greater force on the walls. If the temperature and pressure of the gas inside the container continue to rise, the force that the gas exerts on the container may eventually become too great for the container to withstand, causing it to rupture or explode. This is why it is important to be cautious when working with gases, especially at high temperatures and pressures. While performing such a thought experiment is not recommended in practice due to the potential dangers involved, it is indeed a useful way to understand the behavior of gases and the relationship between temperature, pressure, and volume.

This is a fun and simple experiment that can be done at home to demonstrate the effect of temperature on air pressure.

As the air inside the plastic bottle cools down in the freezer, the gas molecules inside the bottle lose kinetic energy, and hence move more slowly. This causes the pressure of the air inside the bottle to decrease, leading to the dents in the bottle.

When the bottle is taken out of the freezer and the air inside it warms up again, the gas molecules gain kinetic energy and move faster, leading to an increase in the pressure of the air inside the bottle. This increase in pressure causes the bottle to un-dent itself, returning to its original shape.

This experiment is a great way to visually understand the relationship between temperature, pressure, and volume of gases, and can be a fun activity for kids and adults alike. However, it's important to note that the pressure inside the bottle can become dangerously high if the bottle is left in the freezer for too long, so it's important to be cautious and not leave the bottle in the freezer for too long.

## Examples of using the gas pressure-temperature relationship

It's important to remember that the pressure and temperature of a gas are closely related and that changes in one will affect the other. The pressure of a gas is caused by the collisions of the gas particles with the walls of the container, and the temperature of the gas is determined by the average kinetic energy of the gas particles.

When working with gases in a closed container of constant volume, heating the container will cause the gas temperature to increase, which in turn will cause the gas pressure to increase. On the other hand, cooling the container will cause the gas temperature to decrease, which will cause the gas pressure to decrease.

By measuring the pressure of the gas inside the container, we can infer information about the temperature of the gas. This relationship between pressure and temperature is important in many scientific and engineering applications, from studying the behavior of gases to designing and operating industrial processes.

## Gas Pressure and Temperature

How does temperature affect gas pressure?

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.

How does temperature change with 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.

What causes gas pressure and temperature to change?

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.

What happens to gas when the temperature increases?

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).

What is the equation and formula for calculating gas pressure and temperature?

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.

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