Gas equation of state and shape of container

In summary, the equation of state of a gas of interacting particles may depend on the shape of the container, especially if the interaction force is gravity. While the pressure on the wall of a spherical container is determined by the volume and temperature of the gas, the pressure in a box may not be uniform due to the varying distances from the center. The equation of state for a gas of gravitating particles is more complex and involves factors such as density and weak interactions, as shown by the work of Van der Waals.
  • #1
techmologist
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Does the equation of state of a gas of interacting particles depend on the shape of the container they are in? For instance, if the interaction force is gravity (a central force) and the particles are in a spherical container, then it seems reasonable that the pressure on the wall of the container is determined by the volume of the sphere and temperature of the gas. But if the gas is in a box, it isn't obvious to me that the pressure would be the same everywhere on the walls, because the corners of the box are farther away from the center and fewer particles would be there.

By the way, if someone could tell me how to derive the equation of state of a gas of gravitating particles I would be grateful.
 
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  • #2
What has it got to do with the center of the box? Anyway, with the effect of gravity, air particles are slightly weighed downwards. However, it's erratic movement in the volume is what gives it pressure. Nothing to do with the shape.

I'm assuming you're talking about the equation for an ideal gas. You just need Boyle's law and Charles' Law.
 
  • #3
You are also assuming that the gas molecules are not moving inside the container. For a box, it is just as likely that you will find molecules of a gas in the corners as in the center of the box. The pressure and temperature of a gas are related to the motion of the molecules of the gas.
 
  • #4
I'm not talking about an ideal gas. In an ideal gas, the particles don't interact in any way. I'm talking about particles that exert gravitational force on each other. They are not in an external gravitational field.
 
  • #5
Maybe this problem is harder than I thought. Some googling told me that Van der Waals got the Nobel Prize for finding the approximate equation of state assuming a weak interaction (where the shape of the container is irrelevant, and the density is close to uniform).
 

1. What is the gas equation of state and how is it related to the shape of the container?

The gas equation of state, also known as the ideal gas law, is a mathematical relationship between the pressure, volume, temperature, and number of moles of a gas. It states that for a given amount of gas, the product of its pressure and volume is directly proportional to its temperature. The shape of the container does not affect the gas equation of state, as long as the gas behaves ideally.

2. How does the shape of the container affect the behavior of a gas?

The shape of the container can affect the behavior of a gas in two main ways. First, the shape can determine the amount of space available for the gas to expand or contract, which can affect the pressure and volume of the gas. Second, the shape can create areas of high or low pressure within the container, which can affect the movement and distribution of the gas molecules.

3. Can the gas equation of state be applied to real gases?

The ideal gas law is a simplified model that assumes gases behave ideally, meaning they have no volume and do not interact with each other. Real gases, however, do have volume and do interact with each other, so the ideal gas law is not always accurate. However, it can still be used as an approximation for many real gases under certain conditions.

4. How does temperature affect the shape of a container in relation to the gas equation of state?

According to the ideal gas law, temperature is directly proportional to the pressure and volume of a gas. This means that as temperature increases, the pressure and/or volume of the gas will also increase. This can cause the shape of the container to change, as the gas molecules will need more space to move around and exert more pressure on the walls of the container.

5. How does the number of moles of gas in a container affect its shape?

The number of moles of gas in a container does not directly affect its shape. However, it does affect the pressure and volume of the gas, which can indirectly affect the shape of the container. According to the ideal gas law, an increase in the number of moles of gas will result in an increase in pressure and/or volume, which can cause the container to expand or contract.

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