University Physics III · Temperature and Kinetic Theory · 6.03
The ideal-gas equation of state
The equation of state in mole and molecule forms, moles from mass or particle count, isothermal, isobaric, and isochoric changes on p-V and p-T diagrams, and absolute temperature throughout; valid only where molecular volume and attraction are negligible.
Build the model
Connect the measurement to the mechanism.
The equation of state in mole and molecule forms, moles from mass or particle count, isothermal, isobaric, and isochoric changes on p-V and p-T diagrams, and absolute temperature throughout; valid only where molecular volume and attraction are negligible. Treat this course-map statement as a claim to test rather than an invitation to import a familiar equation. In Temperature and Kinetic Theory, begin from microscopic-to-macroscopic derivation, then state the system, observable, assumptions, and evidence before calculating.
- Simple definition
- The equation of state in mole and molecule forms, moles from mass or particle count, isothermal, isobaric, and isochoric changes on p-V and p-T diagrams, and absolute temperature throughout; valid only where molecular volume and attraction are negligible.
- Example
- A strong response uses speed-distribution curves and states where the model stops being reliable.
The model is accurate for sufficiently dilute gases away from phase changes.
Use absolute temperature and consistent SI units.
The subsection's claim
The equation of state in mole and molecule forms, moles from mass or particle count, isothermal, isobaric, and isochoric changes on p-V and p-T diagrams, and absolute temperature throughout; valid only where molecular volume and attraction are negligible.
How to work with it
Start from microscopic-to-macroscopic derivation. Then declaring the gas model and the temperature scale before substituting, and separating a mean of squares from the square of a mean. Select an equation only after its variables and assumptions match the stated system.
What evidence would decide
What absolute-zero intercept and uncertainty do constant-volume pressure-temperature data support? Useful evidence includes pressure-temperature pairs, a linear fit with residuals, the extrapolated intercept, propagated uncertainty, and a dead-volume systematic check.
Keep the boundary visible
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.
Change one variable at a time
Make the relationship visible.
Change volume and temperature separately. Inverse proportionality requires n and T to stay fixed.
PRESSURE166.3 kPa
pV2494.2 kPa L
Live interpretationPRESSURE: 166.3 kPa. pV: 2494.2 kPa L
Catch the common trap
Explain before calculating.
Which temperature belongs in pV=nRT?
Choose an answer to test the model.
Practice & worked examples
Reason from the model, then test the result.
Worked calculationFind the pressure of 0.500 mol of an ideal gas at 300 K in 12.0 L.
- Convert V=12.0 L=0.0120 m³.
- Use p=nRT/V.
- p=(0.500)(8.314)(300)/0.0120=1.04×10⁵ Pa.
AnswerThe pressure is 1.04×10⁵ Pa, or 104 kPa.
TransferDesign one observation that separates The ideal-gas equation of state from Kinetic model of gas pressure.
- Name the observable central to The ideal-gas equation of state.
- Name the contrasting observable or condition in Kinetic model of gas pressure.
- Choose a graph feature, sign, scale, or limiting case that would distinguish them.
AnswerThe comparison is useful only if the proposed observation could rule out at least one of the two accounts.