Physics 7A DL 11 Overview DL 11
Brief Overview
All three of these activities focus on making sense of the construct of modes and the principle of
equipartition and how these constructs relate to the macroscopic constructs phase and thermal energy.
Activities
Activity 3.9 Follow-up of DL 10 FNTs: Modes and Equipartition
Purpose:
• Practice using the construct of mode and determining the number of modes, and thus the thermal
energy, in a variety of physical systems.
Learning Outcomes:
• Develop a representation of thermal energy in a solid and liquid, modeled with each atom or
molecule as being connected to three independent springs, one for each spatial dimension.
• Achieve an understanding of the equipartition of thermal energy into modes with each mode
1
having an average value equal to 𝐸𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑝𝑒𝑟 𝑚𝑜𝑑𝑒 = 2 𝑘𝐵 𝑇.
• Achieve an understanding of the relation of thermal energy to temperature using the Particle
Model of Thermal Energy.
• Achieve an understanding of the relationship between kinds of modes present, the kind of
molecules in the substance, and the phase of the substance.
Activity 3.10 Counting Modes for Monatomic and Polyatomic Gases
Purpose:
• Develop a method for counting modes for gases of single atoms or polyatomic molecules.
Learning Outcomes:
• Discuss the number of modes for a monatomic gas.
• Understand the types of modes that a molecule can have.
• Understand the difference between translational, rotational, and vibrational kinetic energy modes.
• Discuss when potential energy modes can be present.
• Find a general expression for calculating number of possible modes for a polyatomic molecule.
Activity 3.11 Using Modes to Interpret Data
Purpose:
• An Atoms-In-Motion (AIM) simulation provides data that is not ordinarily available in a
macroscopic experiment. In this exercise, the total energy of the particles is known directly,
whereas in a macroscopic experiment, only changes in total energy are available. In this activity,
you will make connections between the Three-Phase Model, the Energy vs. Temperature graph,
and the slope of this graph to the number of modes in each phase.
Learning Outcomes:
• Increased understanding of the connections between representations using an Energy vs.
Temperature graph, phase transitions, bond energy, thermal energy, and the construct “modes”.
• Ability to determine the number of modes in a particular phase from information available on an
Energy vs. Temperature graph
Unit 3: Applying Particle Models to Matter DL 11
, Physics 7A Activity 3.9 DL 11
Follow-up of DL 10 FNTs: Modes and Equipartition
A) FNT 1:
Your TA will assign you a part of this FNT. In addition to answering the following questions, write down
the total thermal energy for the systems being compared in each part.
a) This comparison illustrates the relationship between 𝐸𝑡ℎ𝑒𝑟𝑚𝑎𝑙 and temperature. What other factors
affect the comparison of thermal energy?
b) In terms of our Particle Model of Thermal Energy, why do the two moles of a monatomic solid at
273K have more thermal energy than the one mole at 273K? Be explicit.
c) Defend your choice for this part. Be explicit about the number and type of modes.
d) If you doubled the number of atoms, how would 𝐸𝑡ℎ𝑒𝑟𝑚𝑎𝑙 change?
e) Does a monatomic solid always has more thermal energy than a monatomic gas at the same
temperature?
f) List all possible modes for each gas.
Whole Class Discussion
B) FNT 2:
Discuss, come to a consensus and put your groups’ response to both parts (a) and (b) on the board.
Whole Class Discussion
C) FNT 3:
Discuss, come to a consensus and make sure everyone in your group is prepared to explain your
group’s response to this FNT.
FNT 4:
Write your expressions for the total potential and kinetic energies for a monatomic gas on the board.
Make sure everyone is prepared to explain the expressions relating 𝐾𝐸𝑡𝑜𝑡 and 𝑃𝐸𝑡𝑜𝑡 to 𝐸𝑡ℎ𝑒𝑟𝑚𝑎𝑙 and
𝐸𝑏𝑜𝑛𝑑 in both solids/liquids and in gases, and why the same expression works for both solids and
liquids.
Whole Class Discussion
Unit 3: Applying Particle Models to Matter DL 11
Brief Overview
All three of these activities focus on making sense of the construct of modes and the principle of
equipartition and how these constructs relate to the macroscopic constructs phase and thermal energy.
Activities
Activity 3.9 Follow-up of DL 10 FNTs: Modes and Equipartition
Purpose:
• Practice using the construct of mode and determining the number of modes, and thus the thermal
energy, in a variety of physical systems.
Learning Outcomes:
• Develop a representation of thermal energy in a solid and liquid, modeled with each atom or
molecule as being connected to three independent springs, one for each spatial dimension.
• Achieve an understanding of the equipartition of thermal energy into modes with each mode
1
having an average value equal to 𝐸𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑝𝑒𝑟 𝑚𝑜𝑑𝑒 = 2 𝑘𝐵 𝑇.
• Achieve an understanding of the relation of thermal energy to temperature using the Particle
Model of Thermal Energy.
• Achieve an understanding of the relationship between kinds of modes present, the kind of
molecules in the substance, and the phase of the substance.
Activity 3.10 Counting Modes for Monatomic and Polyatomic Gases
Purpose:
• Develop a method for counting modes for gases of single atoms or polyatomic molecules.
Learning Outcomes:
• Discuss the number of modes for a monatomic gas.
• Understand the types of modes that a molecule can have.
• Understand the difference between translational, rotational, and vibrational kinetic energy modes.
• Discuss when potential energy modes can be present.
• Find a general expression for calculating number of possible modes for a polyatomic molecule.
Activity 3.11 Using Modes to Interpret Data
Purpose:
• An Atoms-In-Motion (AIM) simulation provides data that is not ordinarily available in a
macroscopic experiment. In this exercise, the total energy of the particles is known directly,
whereas in a macroscopic experiment, only changes in total energy are available. In this activity,
you will make connections between the Three-Phase Model, the Energy vs. Temperature graph,
and the slope of this graph to the number of modes in each phase.
Learning Outcomes:
• Increased understanding of the connections between representations using an Energy vs.
Temperature graph, phase transitions, bond energy, thermal energy, and the construct “modes”.
• Ability to determine the number of modes in a particular phase from information available on an
Energy vs. Temperature graph
Unit 3: Applying Particle Models to Matter DL 11
, Physics 7A Activity 3.9 DL 11
Follow-up of DL 10 FNTs: Modes and Equipartition
A) FNT 1:
Your TA will assign you a part of this FNT. In addition to answering the following questions, write down
the total thermal energy for the systems being compared in each part.
a) This comparison illustrates the relationship between 𝐸𝑡ℎ𝑒𝑟𝑚𝑎𝑙 and temperature. What other factors
affect the comparison of thermal energy?
b) In terms of our Particle Model of Thermal Energy, why do the two moles of a monatomic solid at
273K have more thermal energy than the one mole at 273K? Be explicit.
c) Defend your choice for this part. Be explicit about the number and type of modes.
d) If you doubled the number of atoms, how would 𝐸𝑡ℎ𝑒𝑟𝑚𝑎𝑙 change?
e) Does a monatomic solid always has more thermal energy than a monatomic gas at the same
temperature?
f) List all possible modes for each gas.
Whole Class Discussion
B) FNT 2:
Discuss, come to a consensus and put your groups’ response to both parts (a) and (b) on the board.
Whole Class Discussion
C) FNT 3:
Discuss, come to a consensus and make sure everyone in your group is prepared to explain your
group’s response to this FNT.
FNT 4:
Write your expressions for the total potential and kinetic energies for a monatomic gas on the board.
Make sure everyone is prepared to explain the expressions relating 𝐾𝐸𝑡𝑜𝑡 and 𝑃𝐸𝑡𝑜𝑡 to 𝐸𝑡ℎ𝑒𝑟𝑚𝑎𝑙 and
𝐸𝑏𝑜𝑛𝑑 in both solids/liquids and in gases, and why the same expression works for both solids and
liquids.
Whole Class Discussion
Unit 3: Applying Particle Models to Matter DL 11
