Phase cells and equilibrium speed distribution

In summary, in order to determine the equilibrium distribution of molecular speeds in a pure gas, we need to know the probability of each molecule occupying a phase cell and the atomic mass of the molecule. Additionally, we need to know the absolute temperature and the value of B in the equation f(v) = Bv^2 * e^(-mv^2/2kT).
  • #1
michelle001
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Homework Statement


If the probability of any given molecule occupying any given phase cell is known, what additional information is required in order to work out the equilibrium distribution of molecular speeds in a pure gas?

Homework Equations



The Attempt at a Solution


Since the phase cells describe the position and velocity of each molecule - the speed of every molecule can be determined so long as the atomic mass is know. Since we know all phase cells we know number of molecules and the probability of each and can find the spread of speeds. So the only additional information required from that supplied in the question is the atomic mass of the molecule

I can't actually find any information to support this but having tried to figure it out and reread books for last two hours I thought I'd try my first post! can anyone help me??

or having had another think am I supposed to use f(v)=Bv^2 . e^(-mv^2/2kT) in which case I'd need the absolute temperature and atomic mass of neon?

thanks
 
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  • #2
Hi Michelle
I'm not an expert, but I think we're doing the same course.

If you look at the equation that you stated for the speed distribution function f(v), you need to work out what the different parts of it relate to. e^-mv^2/2kT corresponds to the probability of a molecule being found in a given phase cell, so have a think about what other items of information are needed to find f(v).
Hope that helps
 

FAQ: Phase cells and equilibrium speed distribution

1. What do "phase cells" refer to in equilibrium speed distribution?

Phase cells are a way of visualizing the distribution of particles in a gas or liquid at equilibrium. Each phase cell represents a group of particles with similar speeds and directions of motion. Together, these phase cells make up the overall equilibrium speed distribution.

2. How are phase cells related to the Maxwell-Boltzmann distribution?

The Maxwell-Boltzmann distribution describes the probability of finding particles with a particular speed in a gas or liquid at equilibrium. Phase cells are a visual representation of this distribution, with each phase cell representing a group of particles with similar speeds. Thus, phase cells and the Maxwell-Boltzmann distribution are closely related.

3. What is the significance of equilibrium speed distribution in thermodynamics?

The equilibrium speed distribution is a fundamental concept in thermodynamics, as it helps us understand the behavior of particles in a gas or liquid at equilibrium. It allows us to make predictions about the properties of a system, such as temperature, pressure, and energy, based on the distribution of particle speeds.

4. How does the temperature of a system affect the equilibrium speed distribution?

The temperature of a system is directly related to the average speed of particles in that system. As the temperature increases, the average speed of particles also increases, leading to a broader and higher equilibrium speed distribution. Similarly, a decrease in temperature results in a narrower and lower distribution.

5. Can the equilibrium speed distribution be affected by external factors?

Yes, the equilibrium speed distribution can be influenced by external factors such as changes in pressure, volume, or the addition of other substances. These factors can alter the average speed of particles and, in turn, affect the shape and height of the equilibrium speed distribution.

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