Energy and Entropy: Winter-2026
HW 1 : Due Day 2 W1 D3

1. Name the Experiment 2 S0 5453S Consider the following derivative: \begin{align} \left(\frac{\partial {V}}{\partial {S}}\right)_{T} \end{align} Design an experiment to measure this derivative. In your answer, include a schematic of the aperatus and label the quantitites you would measure. Describe your measurement process, and show the algebra required to convert your directly measured quantities into the derivative.
2. Checking for Intensiveness / Extensiveness S0 5453S

   For each of the following equations, check whether it could possibly make sense. You will need to check both dimensions and whether the quantities involved are intensive or extensive. For each equation, explain your reasoning.

   You may assume that quantities with subscripts such as \(V_0\) have the same dimensions and intensiveness/extensiveness as they would have without the subscripts.

   1. \[p = \frac{N^2k_BT}{V}\]

   2. \[p = \frac{Nk_BT}{V}\]

   3. \[U = \frac32 k_BT\]

   4. \[U = - Nk_BT \ln\frac{V}{V_0}\]

   5. \[S = - k_B \ln\frac{V}{V_0}\]

   6. \[S = - k_B \ln\frac{V}{N}\]