These lecture notes covering week 8 of https://paradigms.oregonstate.edu/courses/ph441 include a small group activity in which students derive the Carnot efficiency.

This short lecture precedes osharmonicproj.

Let's apply the relationship of heat, entropy, and temperature to a contemporary challenge!

We'd like to maximize the efficiency of any process that is based on heat flow as an input.

engines.png"/>

Energy flow diagram

The efficiency of the machine is \begin{align} \text{efficiency} &= \frac{W}{Q_{\text{in}}} \\ \textit{e.g.} &=\frac{500\text{ J}}{1000\text{ J}} = 50\% \end{align} For a car engine, \(T_H\approx 600\text{ K}\) and \(T_C\approx 300\text{ K}\).

Remember that \(\Delta S=\frac{Q}{T}\), and \(\Delta S_{\text{tot}} \ge 0\).