**4. Kittel Ch3-4. Energy fluctuations.** Consider a system of fixed volume in thermal contact with a reservoir. Show that the mean square fluctuation in the energy of the system is \[\langle (\varepsilon - \langle \varepsilon \rangle)^2 \rangle = \tau^2 \left( \partial U / \partial \tau \right)_V\](89)Here, \( U \) is the conventional symbol for \( \langle \varepsilon \rangle \). *Hint:* Use the partition function \( Z \) to relate \( \partial U / \partial \tau \) to the mean square fluctuation. Also, multiply out the term \( (..)^2 \).

4. Kittel Ch3-4. Energy fluctuations. Consider a system of fixed volume in thermal contact with a reservoir. Show that the mean square fluctuation in the energy of the system is ((x − (e))²) = t² (JU /ƏT), Here U is the conventional symbol for (e). Hint: Use the partition function Z to relate U/ar to the mean square fluctuation. Also, multiply out the term (...)². (89)

4. Kittel Ch3-4. Energy fluctuations. Consider a system of fixed volume in thermal contact with a reservoir. Show that the mean square fluctuation in the energy of the system is ((x − (e))²) = t² (JU /ƏT), Here U is the conventional symbol for (e). Hint: Use the partition function Z to relate U/ar to the mean square fluctuation. Also, multiply out the term (...)². (89)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

**4. Kittel Ch3-4. Energy fluctuations.** Consider a system of fixed volume in thermal contact with a reservoir. Show that the mean square fluctuation in the energy of the system is

\[
\langle (\varepsilon - \langle \varepsilon \rangle)^2 \rangle = \tau^2 \left( \partial U / \partial \tau \right)_V
\]

(89)

Here, \( U \) is the conventional symbol for \( \langle \varepsilon \rangle \). *Hint:* Use the partition function \( Z \) to relate \( \partial U / \partial \tau \) to the mean square fluctuation. Also, multiply out the term \( (..)^2 \).

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