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 simulationScope & 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
Assumptions to state
State the system, observable, approximation, and conditions held fixed before using a model.
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.
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.
Model, evidence, and boundary
What is the strongest test of a claim about Equipartition and molar heat capacities of gases?
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.
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.