3. Kittel, Ch4-7. Free energy of photon gas. (a) Show that the partition function of a photon gas is given by z = II n II [1-exp(-ħw/T)]¯'. where the product is over the modes n. (b) The Helmholtz free energy is found directly from (53) as F = T log[1-exp(-ħw, /T)]. F = 71 Transform of the sum to an integral; integrate by parts to find T² VT (53) 3 3 45h³c³ (54) (55)
3. Kittel, Ch4-7. Free energy of photon gas. (a) Show that the partition function of a photon gas is given by z = II n II [1-exp(-ħw/T)]¯'. where the product is over the modes n. (b) The Helmholtz free energy is found directly from (53) as F = T log[1-exp(-ħw, /T)]. F = 71 Transform of the sum to an integral; integrate by parts to find T² VT (53) 3 3 45h³c³ (54) (55)
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![3. Kittel, Ch4-7. Free energy of photon gas. (a) Show that the partition function of a
photon gas is given by
z = II
n
II [1-exp(-ħw/T)]¯'.
where the product is over the modes n. (b) The Helmholtz free energy is found
directly from (53) as
F = T log[1-exp(-ħw, /T)].
F =
71
Transform of the sum to an integral; integrate by parts to find
T² VT
3 3
45ħ³c³
(53)
(54)
(55)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2F442fcce1-62ac-4bbb-9709-c1fbe38dd7e1%2F63kbi2t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Kittel, Ch4-7. Free energy of photon gas. (a) Show that the partition function of a
photon gas is given by
z = II
n
II [1-exp(-ħw/T)]¯'.
where the product is over the modes n. (b) The Helmholtz free energy is found
directly from (53) as
F = T log[1-exp(-ħw, /T)].
F =
71
Transform of the sum to an integral; integrate by parts to find
T² VT
3 3
45ħ³c³
(53)
(54)
(55)
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