Partition Function Homework: Find En at 290K

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Homework Help Overview

The problem involves calculating the partition function for a system at a temperature of 290 K, where the energy of the nth state is given by En = n(0.01 eV). Participants are exploring the relationship between energy states and the partition function in the context of statistical mechanics.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the expression for the partition function and the implications of the energy state formula. There is confusion regarding the units of energy and the Boltzmann constant, leading to questions about how to properly align these units for calculations.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the energy state expression and address unit compatibility issues. Some guidance has been offered regarding unit conversion, but no consensus has been reached on the next steps for solving the problem.

Contextual Notes

There is a noted discrepancy in the units being used for energy and temperature, which is affecting the participants' ability to proceed with the calculation of the partition function.

lmanri
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Homework Statement


Consider a system at 290 K for which the energy of the nth state is En=n(.01 eV). Using 1+a+a2+a3...=1/(1-a) for a <1 where necessary, Find the value of the partition function.


Homework Equations



The Attempt at a Solution




Z=∑e-βE[itex]_{}n[/itex]

β=1/κT

I don't know what the energy of the state would be so I can't figure out the problem.
 
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What do you mean you don't know what the energy of the state is? You wrote it already: E(n) = (0.01 eV)*n. It is linear in n.
 
So, I would then have
Z=(sum)e^(-(1/((1.38*10^-23)(290)))(n(0.01))
 
No. You have incompatible units.
 
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I don't understand it.
 
tman means, your units of energy is in eV, but your Boltzmann constant is using units of J/K. You should convert one or the other to have the same units.
 
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Oh ok, which is 8.625*10^-5 eV/K
 

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