Ideal gas inside a sphere under the influence of gravitational field

In summary, the conversation discusses an ideal gas system consisting of N classical particles inside a spherical bottle with a radius of R and in thermal equilibrium with a heat reservoir at temperature T. The objective is to find the partition function and energy of the system. The person facing the problem is unsure about the potential energy of a single particle, particularly in regards to using spherical coordinates. They clarify that the potential energy depends on the height of the particle, not its distance from the origin.
  • #1
Thunderbird88
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0

Homework Statement



We have an ideal gas consisted of N classical particles, each having mass m. The system is inside a spherical bottle of radius R and is inside the gravitational field of the earth. The system is also in thermal equilibrium with a heat reservoir which has temperature T. I have to find the partition function and the energy of the system.2. The attempt at a solution

The problem I face is finding the energy of a single particle. I'm confused regarding the potential energy. My solution is in the pdf file. Is there something wrong with the spherical coordinates?
 

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  • #2
I'm assuming you're placing the origin of the coordinate system in the middle of the sphere and directing the z-axis upward. The potential energy depends on how high the particle is, not how far it is from the origin, so U=mgr isn't correct.
 

What is an ideal gas?

An ideal gas is a theoretical gas that follows the gas laws (Boyle's law, Charles' law, and Avogadro's law) under all conditions of temperature and pressure. It assumes that there are no intermolecular forces between the gas particles and that the volume of the particles themselves is negligible.

What is a sphere under the influence of gravitational field?

A sphere under the influence of gravitational field refers to a spherical object that is subject to the force of gravity. This means that the object has a mass and is located in a region where there is a gravitational field, causing it to experience a force of attraction towards the center of the field.

How does the gravitational field affect an ideal gas inside a sphere?

The gravitational field affects the ideal gas inside a sphere by causing the gas particles to experience a force of attraction towards the center of the sphere. This force changes the distribution of the gas particles, leading to a higher concentration of particles towards the center of the sphere.

What is the relationship between pressure and volume in an ideal gas inside a sphere under the influence of gravitational field?

The relationship between pressure and volume in an ideal gas inside a sphere under the influence of gravitational field follows Boyle's law, which states that at a constant temperature, the pressure of a gas is inversely proportional to its volume. This means that as the volume of the gas decreases, the pressure increases, and vice versa.

How does temperature affect an ideal gas inside a sphere under the influence of gravitational field?

Temperature affects an ideal gas inside a sphere under the influence of gravitational field by changing the average kinetic energy of the gas particles. As the temperature increases, the gas particles move faster, leading to an increase in pressure and volume. On the other hand, a decrease in temperature results in slower-moving particles and a decrease in pressure and volume.

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