(a) Show that: ´Ə In Z = kT² (b) Show that: 1 (&z' < E² > (c) Recall the definition of heat capacity at constant volume: au Cy = aT %3D
(a) Show that: ´Ə In Z = kT² (b) Show that: 1 (&z' < E² > (c) Recall the definition of heat capacity at constant volume: au Cy = aT %3D
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Transcribed Image Text:Consider a canonical ensemble.
(a) Show that:
Ə In Z
<E > = kT²
ƏT
(b) Show that:
< E² >
z (aB2
(c) Recall the definition of heat capacity at constant volume:
Cp =
aT
In the case of a canonical ensemble, <E> is used for U in the above expression. Perform the necessary
partial differentiation to obtain an expression for C, in terms of <E?>, <E>, and kT.
(d) Suppose we define:
SE = E – < E >
Show that:
< (SE)² >
kT²
(e) Show that:
-d < E >
< E² > - < E >²=
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