Question

Problem 3: A particle can exist in levels of energy 0, $\epsilon$, $2\epsilon$, and $3\epsilon$ having degeneracies (number of microstate) 1, 3, 3, and 1 respectively. Show that Helmholtz function F can be expressed as F = $-3k_BT \ln(1 + \exp(-\epsilon/k_BT))$

          Problem 3:
A particle can exist in levels of energy 0, $\epsilon$, $2\epsilon$, and $3\epsilon$ having degeneracies (number of
microstate) 1, 3, 3, and 1 respectively.
Show that Helmholtz function F can be expressed as
F = $-3k_BT \ln(1 + \exp(-\epsilon/k_BT))$

Problem 3:
A particle can exist in levels of energy 0, ϵ, 2ϵ, and 3ϵ having degeneracies (number of
microstate) 1, 3, 3, and 1 respectively.
Show that Helmholtz function F can be expressed as
F = -3kBT ln(1 + (-ϵ/kBT))

Added by Consuelo W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

09/25/2023

Step 1

Step 1: The Helmholtz function F is defined as F = U - TS, where U is the internal energy, T is the temperature, and S is the entropy. Show more…

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Problem 3: A particle can exist in levels of energy 0, e^2c, and 3c having degeneracies number of microstates 1, 3, and 1 respectively. Show that Helmholtz function F can be expressed as F = -3kBTln(1+exp(-c/kBT))