Activity: Basics of heat engines
This brief lecture covers the basics of heat engines.
- face Lecture 10 min. Student handout (PDF)
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Media
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.
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 \(\Delta S_{\text{tot}} \ge 0\).
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face Lecture
30 min.
A coarse-grained model for transportation
Contemporary Challenges 2021 (4 years) A short lecture introducing the idea that most of the energy loss when driving is going into the kinetic energy of the air. - assignment Heat pump
assignment Homework
Heat pump
Carnot efficiency Work Entropy Heat pump Thermal and Statistical Physics 2020Show 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 Work, Heat, and cycles
face Lecture
120 min.
Work, Heat, and cycles
Thermal and Statistical Physics 2020work 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 Grey space capsule
group Small Group Activity
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Grey space capsule
Contemporary Challenges 2021 (4 years) In this small group activity, students work out the steady state temperature of an object absorbing and emitting blackbody radiation. - group Heat capacity of N$_2$
group Small Group Activity
30 min.
Heat capacity of N2
Contemporary Challenges 2021 (4 years) Students sketch the temperature-dependent heat capacity of molecular nitrogen. They apply the equipartition theorem and compute the temperatures at which degrees of freedom “freeze out.” - face Equipartition theorem
face Lecture
30 min.
Equipartition theorem
Contemporary Challenges 2021 (4 years) This lecture introduces the equipartition theorem. - face Introducing entropy
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Introducing entropy
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group Small Group Activity
30 min.
Energy radiated from one oscillator
Contemporary Challenges 2021 (4 years) This lecture is one step in motivating the form of the Planck distribution. - group Black space capsule
group Small Group Activity
30 min.
Black space capsule
Contemporary Challenges 2022 (3 years) In this activity, students apply the Stefan-Boltzmann equation and the principle of energy balance in steady state to find the steady state temperature of a black object in near-Earth orbit. - group Earthquake waves
group Small Group Activity
30 min.
Earthquake waves
Contemporary Challenges 2021 (4 years) In this activity students use the known speed of earthquake waves to estimate the Young's modulus of the Earth's crust.
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