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Stirling’s ApproximationI’m studying and need help with a Chemical Engineering question to help me learn.Hi I need help with a problem using Stirling’s approximation. Please take a look at the pdf file that explains the problem.3
2
Problem 2 [10 points]
We found (or accepted as an article of faith) that
Ω(E, N, V ) ≈ V N ·
=
1
h3N
·
2π 3N/2
∆√
2mE ·
(2mE)(3N −1)/2
2E
Γ(3N/2)
3N/2
∆ 1
N (2πmE)
V
2E h3N
Γ(3N/2)
(7)
Assume, E = 3N kB T /2, (where kB is the Boltzmann constant), and T = 300 K. Further,
assume y m = 10−25 kgs, a = 0.1 m, N = 6.02 × 1023 , and ∆ = 0.01E. Estimate Ω. (You will need
to use Stirling’s approximation.)

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