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University Physics III

University Physics III · Temperature and Kinetic Theory · 6.08

Equipartition and molar heat capacities of gases

One-half kT per quadratic degree of freedom, giving three-halves R for a monatomic gas and five-halves R for a diatomic one with vibration frozen out, the ideal-gas result that constant-pressure and constant-volume molar heat capacities differ by R, and their ratio gamma; the constant-pressure result is quoted here and derived once the first law is available, and the classical count fails wherever modes freeze out.

Course-map guide · not a complete lesson or simulation

Scope & orientation

What this subsection covers

One-half kT per quadratic degree of freedom, giving three-halves R for a monatomic gas and five-halves R for a diatomic one with vibration frozen out, the ideal-gas result that constant-pressure and constant-volume molar heat capacities differ by R, and their ratio gamma; the constant-pressure resu…

A strong response uses expansion and thermal-stress sketches and states where the model stops being reliable.

Reasoning checklist

Evidence, assumptions and limits

01

Assumptions to state

State the system, observable, approximation, and conditions held fixed before using a model.

02

Evidence to collect

Does a simulated gas of elastic spheres relax to the speed distribution its temperature predicts?

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Does a simulated gas of elastic spheres relax to the speed distribution its temperature predicts? Useful evidence includes speed histograms against time, fitted most-probable and rms speeds, particle-number and step-size convergence, energy conservation, and a hard-sphere limitation.

03

Limits to state

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus.

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This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. Third-semester content is the least standardised of the introductory sequence: departments place oscillations, waves, optics, and thermal physics differently, and the modern-physics units here are a bounded survey rather than a complete course in relativity, quantum mechanics, atomic, nuclear, or particle physics. Follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.

Diagram & examples

Work the claim before choosing an equation

Interactive concept map

Follow the model from claim to evidence.

01 · Physical claimEquipartition and molar heat capacities of gases

One-half kT per quadratic degree of freedom, giving three-halves R for a monatomic gas and five-halves R for a diatomic one with vibration frozen out, the ideal-gas result that constant-pressure and constant-volume molar heat capacities differ by R.

Read the complete note

One-half kT per quadratic degree of freedom, giving three-halves R for a monatomic gas and five-halves R for a diatomic one with vibration frozen out, the ideal-gas result that constant-pressure and constant-volume molar heat capacities differ by R, and their ratio gamma; the constant-pressure result is quoted here and derived once the first law is available, and the classical count fails wherever modes freeze out.

02 · RepresentationThe subsection's claim

Model, evidence, and boundary

03 · TestPrediction before measurement

What is the strongest test of a claim about Equipartition and molar heat capacities of gases?

04 · Evidence & boundaryDecide, then qualify

Does a simulated gas of elastic spheres relax to the speed distribution its temperature predicts?

Read the complete note

Does a simulated gas of elastic spheres relax to the speed distribution its temperature predicts? Useful evidence includes speed histograms against time, fitted most-probable and rms speeds, particle-number and step-size convergence, energy conservation, and a hard-sphere limitation.

Interactive diagram for Equipartition and molar heat capacities of gases: follow the physical claim through its representation, proposed test, evidence, and model boundary.

modelModel, evidence, and boundary turns the stated idea into a representation that can make a prediction.

Example questions

Try the reasoning before revealing the structure.

Diagram check

What is the strongest test of a claim about Equipartition and molar heat capacities of gases?

Quick check

Test the reasoning, not recall

What is the strongest test of a claim about Equipartition and molar heat capacities of gases?

Choose an answer to test the model.