Physics 7A DL 13 Overview DL 13
Brief Overview
All three of these activities focus on using key concepts and relationships from multiple models you
now know a lot about: Energy-Interaction Model, Three-Phase Model of Matter, and especially, the
Particle Model of Matter and the Particle Model of Thermal Energy. You will use these relationships
and constructs to develop explanations of thermal processes involving thermal energies of various
substances and explanations of observed values of molar values of heat capacity and the observed trends
of these values across types of substances
Activities
Activity 3.15 Follow-up of FNTs from DL 12: More on Modes and Equipartition
Purpose:
• To provide an opportunity to fully make sense of the values and trends in values of the molar
heat capacities of real substances in terms of the Particle Model of Thermal Energy and the
concept of freezing out of modes at lower temperatures.
Learning Outcomes:
• Solid understanding of the relationship of empirical values of heat capacities of typical gas
phase substances and modes as defined in the Particle Model of Thermal Energy.
• Capable of explaining the temperature dependence of the empirical values of heat capacities of
typical gas phase substances using the ideas of freezing out of modes and the Particle Model of
Thermal Energy.
Model: The Intro Model of Thermodynamics
Activity 4.1 The Intro Model of Thermodynamics: Some Constructs and Relationship
Purpose:
Provide opportunity to become fully acquainted with the concepts of internal energy, state functions,
processes, and state variables.
Learning Outcomes:
• A beginning understanding of the meaning of internal energy.
• A beginning understanding of the first law of thermodynamics, Δ𝑈 = 𝑄 + 𝑊, as another way
of expressing conservation of energy.
• A beginning understanding of what a process is.
• A beginning understanding of what a state function is.
• A beginning understanding of what a state diagram is and how a process is shown on one.
• A beginning understanding of how work is determined from a PV diagram.
Activity 4.2 Constant-Volume Heat Capacity (𝑪𝒗 ) Measurement
Purpose:
• An opportunity to carry out a measurement of the constant volume heat capacity using the Atoms
in Motion simulator.
Learning Outcomes:
• Deeper understanding of the constructs mentioned in the learning outcomes of Act 4.1.
• A solid understanding of what actually happens in a 𝐶𝑣 measurement.
• Make a connection between what is going on at the particle level with what is happening
macroscopically.
Unit 4: Models of Thermodynamics DL 13
, Physics 7A Activity 3.15 DL 13
Follow-up of FNTs from DL 12:
More on Modes and Equipartition
A) FNT 1:
a) Explain how you can tell from the graph of 𝒄𝒗,𝒎𝒐𝒍 /𝑹 as a function of temperature that H2 has more
modes than the monatomic gases at 300 K.
Additional Question: List the active modes in monatomic gases. Knowing that the quantum
splitting of the rotational energies of polyatomic molecules is typically much less than the quantum
splitting of the vibrational energy levels, list the active modes for H2.
b) Explain why the number of modes per particle increases with increasing temperature for all of the
substances except the monatomic gases.
Additional Question: Reasoning from our model, will the heat capacities of polyatomic molecules
in the gas phase increase indefinitely with temperature (assuming the molecules do not dissociate),
or do they reach a maximum value? Is there evidence of this in the data shown in the graph?
c) Which gas (H2 or N2) has the larger energy splitting between the ground state and the first excited
energy level (for the vibrational modes) in the temperature range depicted in the graph?
Additional Question: If the modes of a given molecule are either frozen out or active, why do they
seem to slowly turn on according to the graph? That is, why don’t the lines for H 2 and N2 simply
jump up from 5 to 7 modes at different temperatures instead of gradually increasing?
Whole Class Discussion
B) FNT 2:
Put your responses to parts a)-e) on the board and be ready to discuss in Whole Class Discussion.
Whole Class Discussion
Unit 4: Models of Thermodynamics DL 13
Brief Overview
All three of these activities focus on using key concepts and relationships from multiple models you
now know a lot about: Energy-Interaction Model, Three-Phase Model of Matter, and especially, the
Particle Model of Matter and the Particle Model of Thermal Energy. You will use these relationships
and constructs to develop explanations of thermal processes involving thermal energies of various
substances and explanations of observed values of molar values of heat capacity and the observed trends
of these values across types of substances
Activities
Activity 3.15 Follow-up of FNTs from DL 12: More on Modes and Equipartition
Purpose:
• To provide an opportunity to fully make sense of the values and trends in values of the molar
heat capacities of real substances in terms of the Particle Model of Thermal Energy and the
concept of freezing out of modes at lower temperatures.
Learning Outcomes:
• Solid understanding of the relationship of empirical values of heat capacities of typical gas
phase substances and modes as defined in the Particle Model of Thermal Energy.
• Capable of explaining the temperature dependence of the empirical values of heat capacities of
typical gas phase substances using the ideas of freezing out of modes and the Particle Model of
Thermal Energy.
Model: The Intro Model of Thermodynamics
Activity 4.1 The Intro Model of Thermodynamics: Some Constructs and Relationship
Purpose:
Provide opportunity to become fully acquainted with the concepts of internal energy, state functions,
processes, and state variables.
Learning Outcomes:
• A beginning understanding of the meaning of internal energy.
• A beginning understanding of the first law of thermodynamics, Δ𝑈 = 𝑄 + 𝑊, as another way
of expressing conservation of energy.
• A beginning understanding of what a process is.
• A beginning understanding of what a state function is.
• A beginning understanding of what a state diagram is and how a process is shown on one.
• A beginning understanding of how work is determined from a PV diagram.
Activity 4.2 Constant-Volume Heat Capacity (𝑪𝒗 ) Measurement
Purpose:
• An opportunity to carry out a measurement of the constant volume heat capacity using the Atoms
in Motion simulator.
Learning Outcomes:
• Deeper understanding of the constructs mentioned in the learning outcomes of Act 4.1.
• A solid understanding of what actually happens in a 𝐶𝑣 measurement.
• Make a connection between what is going on at the particle level with what is happening
macroscopically.
Unit 4: Models of Thermodynamics DL 13
, Physics 7A Activity 3.15 DL 13
Follow-up of FNTs from DL 12:
More on Modes and Equipartition
A) FNT 1:
a) Explain how you can tell from the graph of 𝒄𝒗,𝒎𝒐𝒍 /𝑹 as a function of temperature that H2 has more
modes than the monatomic gases at 300 K.
Additional Question: List the active modes in monatomic gases. Knowing that the quantum
splitting of the rotational energies of polyatomic molecules is typically much less than the quantum
splitting of the vibrational energy levels, list the active modes for H2.
b) Explain why the number of modes per particle increases with increasing temperature for all of the
substances except the monatomic gases.
Additional Question: Reasoning from our model, will the heat capacities of polyatomic molecules
in the gas phase increase indefinitely with temperature (assuming the molecules do not dissociate),
or do they reach a maximum value? Is there evidence of this in the data shown in the graph?
c) Which gas (H2 or N2) has the larger energy splitting between the ground state and the first excited
energy level (for the vibrational modes) in the temperature range depicted in the graph?
Additional Question: If the modes of a given molecule are either frozen out or active, why do they
seem to slowly turn on according to the graph? That is, why don’t the lines for H 2 and N2 simply
jump up from 5 to 7 modes at different temperatures instead of gradually increasing?
Whole Class Discussion
B) FNT 2:
Put your responses to parts a)-e) on the board and be ready to discuss in Whole Class Discussion.
Whole Class Discussion
Unit 4: Models of Thermodynamics DL 13
