assignment Homework
energy Boltzmann factor statistical mechanics heat capacity
Thermal and Statistical Physics 2020
Consider a system of
fixed volume in thermal contact with a resevoir. Show that the mean
square fluctuations in the energy of the system is \begin{equation}
\left<\left(\varepsilon-\langle\varepsilon\rangle\right)^2\right>
= k_BT^2\left(\frac{\partial U}{\partial T}\right)_{V}
\end{equation} Here \(U\) is the conventional symbol for
\(\langle\varepsilon\rangle\).
Hint: Use the partition function
\(Z\) to relate \(\left(\frac{\partial U}{\partial T}\right)_V\) to
the mean square fluctuation. Also, multiply out the term
\((\cdots)^2\).