Problem number 4 from Chapter 3 of \"Thermal Physics\" by Kittel& Kroemer Consid

Question

Problem number 4 from Chapter 3 of "Thermal Physics" by Kittel& Kroemer

Consider a system of fixed volume in thermal contact with areservoir. Show that the mean square fluctuation in theenergy of the system is;<(-<>)2=2(U/)V --> referred to as(89). Here U is the conventional symbol for <>. Hint: Use the partition function Z to relateU/ to mean square fluctuation. Also,multiply out the term (...)2Note: Thetemperature of a system is a quantity that by definitiondoes not fluctuate in value when the system is in thermal contactwith a reservoir. Any other attitude would be inconsistentwith our definition of the temperature of a system. Theenergy of such a system may fluctuate, but the temperature doesnot. Some workers do not adhere to a rigorous definition oftemperature. Thus Landau and Lifshitz give the result;<()2 >=2/CV --> referred to as (90), but this should beviewed as just another form of (89) with set equal toU/CV. We know thatU=CV, whence (90) becomes<(U)2>=2CV,which is our result (89).

so we know... F=U+, and Z=sexp(-s/)

so I took the partial derivative of U with respect to , butthis got me nowhere and I honestly have no idea what to donow. Or if I even did the right thing taking that partialderivative...

Explanation / Answer

Okay, so upon reading the question very carefully and disregardingthe Note, I've decided that it's really asking me to justverify equation (89). Is this so? It doesn't really aska question that I can find.

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