LizardWizard
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Homework Statement
For a gas of N fermions with mass M in 2D in a region of area A in thermal equilibrium at temperature T, we are asked to find ##U/N## in fuction of ##T## and ##a=A/N##.
The attempt at a solution
I used ##U=\sum(<n_i>\epsilon_i) = \sum(\exp(\beta(\mu-\epsilon_i))\epsilon_i = \exp(\mu\beta)\sum(\exp(-\epsilon_i\beta)\epsilon_i##
from which ##\exp(\mu\beta)=n/\lambda## where ##n=N/V## and ##\lambda=mkT/2\pi\hbar^2##
Now as you can tell expressing this in terms of ##a## is awkward to say the least, did I go wrong in the calculations somewhere?
For a gas of N fermions with mass M in 2D in a region of area A in thermal equilibrium at temperature T, we are asked to find ##U/N## in fuction of ##T## and ##a=A/N##.
The attempt at a solution
I used ##U=\sum(<n_i>\epsilon_i) = \sum(\exp(\beta(\mu-\epsilon_i))\epsilon_i = \exp(\mu\beta)\sum(\exp(-\epsilon_i\beta)\epsilon_i##
from which ##\exp(\mu\beta)=n/\lambda## where ##n=N/V## and ##\lambda=mkT/2\pi\hbar^2##
Now as you can tell expressing this in terms of ##a## is awkward to say the least, did I go wrong in the calculations somewhere?