This brief lecture covers the basics of heat engines.
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.
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 \(\Delta S_{\text{tot}} \ge 0\).
face Lecture
30 min.
assignment Homework
Show that for a reversible heat pump the energy required per unit of heat delivered inside the building is given by the Carnot efficiency: \begin{align} \frac{W}{Q_H} &= \eta_C = \frac{T_H-T_C}{T_H} \end{align} What happens if the heat pump is not reversible?
Assume that the electricity consumed by a reversible heat pump must itself be generated by a Carnot engine operating between the even hotter temperature \(T_{HH}\) and the cold (outdoors) temperature \(T_C\). What is the ratio \(\frac{Q_{HH}}{Q_H}\) of the heat consumed at \(T_{HH}\) (i.e. fuel burned) to the heat delivered at \(T_H\) (in the house we want to heat)? Give numerical values for \(T_{HH}=600\text{K}\); \(T_{H}=300\text{K}\); \(T_{C}=270\text{K}\).
Draw an energy-entropy flow diagram for the combination heat engine-heat pump, similar to Figures 8.1, 8.2 and 8.4 in the text (or the equivalent but sloppier) figures in the course notes. However, in this case we will involve no external work at all, only energy and entropy flows at three temperatures, since the work done is all generated from heat.
face Lecture
120 min.
work heat engines Carnot thermodynamics entropy
These lecture notes covering week 8 of Thermal and Statistical Physics include a small group activity in which students derive the Carnot efficiency.group Small Group Activity
30 min.
group Small Group Activity
30 min.
face Lecture
30 min.
face Lecture
30 min.
group Small Group Activity
30 min.
group Small Group Activity
30 min.
group Small Group Activity
30 min.