A glass of water

Activity: A glass of water

Energy and Entropy 2021 (2 years)

Students generate a list of properties a glass of water might have. The class then discusses and categorizes those properties.

Small Group Activity schedule 30 min. description Student handout (PDF)
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thermodynamics intensive extensive temperature volume energy entropy

I am using this activity as the very first content in Energy and Entropy. See Naming and Classifying Thermodynamic Variables for a list of earlier versions of this prompt. The idea is to familiarize students with what sorts of properties are considered in thermodynamics.
The key to this particular activity is that we then discuss which are intensive and which are extensive without yet defining those terms. The idea is that by drinking half of the glass of water we make concrete the "doubling the size" that is often discussed when talking about intensive and extensive properties. This also guides us to the set of properties that are used in bulk thermodynamics, since those properties are either intensive or extensive.

We will be spending this course studying thermodynamics, which is the branch of physics that deals with the physical properties of matter and the laws that govern the properties of matter. Today we will be discussing what kinds of properties matter can have.

I'd like you all to start by pouring yourself a cup of water. I'll give you a moment to go to your kitchens. Then in your small groups I'd like you to brainstorm a list of all the properties that cup of water might have. Please limit yourselves to properties of the water itself , omitting any properties of the cup or the room around you.

Drinking half

If you drink half of your glass of water (feel free to do so), how will each of your properties change for the water that remains in the glass?

Spring Force Constant

Homework

Spring Force Constant
Energy and Entropy 2021 (2 years) The spring constant \(k\) for a one-dimensional spring is defined by: \[F=k(x-x_0).\] Discuss briefly whether each of the variables in this equation is extensive or intensive.
Microwave oven Ice Calorimetry Lab

Experiment

60 min.

Microwave oven Ice Calorimetry Lab
Energy and Entropy 2021 (2 years)
heat entropy water ice thermodynamics
In this remote-friendly activity, students use a microwave oven (and optionally a thermometer) to measure the latent heat of melting for water (and optionally the heat capacity). From these they compute changes in entropy. See also Ice Calorimetry Lab.
Pineapples and Pumpkins

Whole Class Activity

10 min.

Pineapples and Pumpkins
Static Fields 2023 (6 years)
Integration Sequence

There are two versions of this activity:
As a whole class activity, the instructor cuts a pumpkin in order to produce a small volume element \(d\tau\), interspersing their work with a sequence of small whiteboard questions. This version of the activity is described here.
As a small group activity, students are given pineapple rounds and pumpkin wedges to explore area volume elements in cylindrical and spherical coordinate systems. In this version of the activity, the fruit is distribued to the students with appropriate children's pumpkin cutting equipment, as part of activities Vector Differential--Curvilinear, Scalar Surface and Volume Elements, or Vector Surface and Volume Elements.
Free expansion

Quiz

60 min.

Free expansion
Energy and Entropy 2021 (2 years)
adiabatic expansion entropy temperature ideal gas
Students will determine the change in entropy (positive, negative, or none) for both the system and surroundings in three different cases. This is followed by an active whole-class discussion about where the entropy comes from during an irreversible process.
Energy and heat and entropy

Lecture

30 min.

Energy and heat and entropy
Energy and Entropy 2021 (2 years)
latent heat heat capacity internal energy entropy
This short lecture introduces the ideas required for Ice Calorimetry Lab or Microwave oven Ice Calorimetry Lab.
Introducing entropy

Lecture

30 min.

Introducing entropy
Contemporary Challenges 2021 (4 years)
entropy multiplicity heat thermodynamics
This lecture introduces the idea of entropy, including the relationship between entropy and multiplicity as well as the relationship between changes in entropy and heat.
Gibbs entropy approach

Lecture

120 min.

Gibbs entropy approach
Thermal and Statistical Physics 2020
Gibbs entropy information theory probability statistical mechanics
These lecture notes for the first week of Thermal and Statistical Physics include a couple of small group activities in which students work with the Gibbs formulation of the entropy.
Chemical potential and Gibbs distribution

Lecture

120 min.

Chemical potential and Gibbs distribution
Thermal and Statistical Physics 2020
chemical potential Gibbs distribution grand canonical ensemble statistical mechanics
These notes from the fifth week of Thermal and Statistical Physics cover the grand canonical ensemble. They include several small group activities.
Inner Product Properties
Homework

Inner Product Properties
None 2023 The properties that an inner product on an abstract vector space must satisfy can be found in: Definition and Properties of an Inner Product. Definition: The inner product for any two vectors in the vector space of periodic functions with a given period (let's pick \(2\pi\) for simplicity) is given by: \[\left\langle {f}\middle|{g}\right\rangle =\int_0^{2\pi} f^*(x)\, g(x)\, dx\]
1. Show that the first property of inner products \[\left\langle {f}\middle|{g}\right\rangle =\left\langle {g}\middle|{f}\right\rangle ^*\] is satisfied for this definition.
2. Show that the second property of inner products \[\left\langle {f}\right|\Big(\lambda\left|{g}\right\rangle + \mu \left|{h}\right\rangle \Big) = \lambda\left\langle {f}\middle|{g}\right\rangle +\mu\left\langle {f}\middle|{h}\right\rangle \] is satisfied for this definition.
Ideal Gas Model

Small Group Activity

30 min.

Ideal Gas Model

Ideal Gas surfaces thermo
Students consider whether the thermo surfaces reflect the properties of an ideal gas.

Learning Outcomes

ph423: 1) Use both dimensional reasoning and intensivity/extensivity to make sense of mathematical expressions involving thermodynamic variables