Boltzmann Distribution: Formula & Fig 2a in Document

In summary, the conversation is discussing the formula used to create the exponential Boltzmann distribution in fig 2a of a document. The formula is y=e^(ln(600)-b*x), where the only free parameter is α. The formula goes through ~600 at βε=0 and can also be written as exp(log(600) - βε).
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  • #2
Doesn't the caption explain it?
 
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Likes vanhees71
  • #3
funny,
But what values to put in?
Around x=1 it seems to get y=200
e^(ln(600)-1/(1.381×10^-23*300)) = 0?
 
  • #4
Since the x-axis is βε, the only free parameter is α. As you realized, it goes through ~600 at βε=0, so the formula being plotted is clearly 600*exp(-βε). Or, if you like, exp(log(600) - βε)
 
  • #5
Doh! So simple, thanks!
 
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Likes Baluncore

FAQ: Boltzmann Distribution: Formula & Fig 2a in Document

What is the Boltzmann Distribution formula?

The Boltzmann Distribution formula is a mathematical equation used to describe the distribution of particles in a system at a given temperature. It is represented as P(E) = (1/Z)e^(-E/kT), where P(E) is the probability of a particle having energy E, Z is the partition function, k is the Boltzmann constant, and T is the temperature.

How is the Boltzmann Distribution related to thermodynamics?

The Boltzmann Distribution is closely related to thermodynamics as it describes the distribution of particles in a system at a given temperature, which is a fundamental concept in thermodynamics. It helps to explain the behavior of particles and their energies in a system, which is essential for understanding various thermodynamic processes.

What does Fig 2a in the document represent?

Fig 2a in the document represents a graphical representation of the Boltzmann Distribution formula. It shows the relationship between the probability of a particle having a certain energy and the energy levels in a system. The curve in the graph represents the probability distribution, with the peak indicating the most probable energy level for particles in the system.

How is the Boltzmann Distribution formula used in practical applications?

The Boltzmann Distribution formula is used in various practical applications, including thermodynamics, statistical mechanics, and quantum mechanics. It is also used in fields such as chemistry and physics to understand the behavior of particles in a system and to calculate various thermodynamic properties, such as entropy and free energy.

What factors affect the Boltzmann Distribution?

The Boltzmann Distribution is affected by several factors, including temperature, energy levels, and the number of particles in a system. As temperature increases, the distribution curve shifts towards higher energy levels, indicating that more particles have higher energies. Similarly, increasing the number of particles or energy levels in a system also affects the distribution curve.

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