Explicit science instruction
For a fixed amount of gas at constant temperature, pressure and volume are inversely related in the ideal model: P₁V₁=P₂V₂.
An inverse relationship means doubling pressure predicts half the volume, not double the volume. A graph of P versus V is curved, while P versus 1/V is linear in the ideal model.
State the controlled conditions before using the equation; if temperature or amount changes, the simple Boyle relation is not sufficient.
Vocabulary: Boyle’s law; inverse relationship; controlled variable; pressure; volume.
Worked example with reasoning
A gas occupies 4.0 L at 1.0 atm. At constant temperature, increasing pressure to 2.0 atm predicts V₂=(1.0×4.0)/2.0=2.0 L.
Guided question
A gas changes from 1.2 atm and 5.0 L to 2.0 atm. Calculate the new volume and identify the assumption that justifies the equation.
Independent work
- Solve four P₁V₁=P₂V₂ problems with units.
- Sketch P versus V and P versus 1/V.
- Explain one experimental change that would invalidate a Boyle-only analysis.
Misconception check
In an inverse relationship, a constant difference is not expected; the product is the conserved proportional quantity.
Formative understanding check
What quantity remains constant in the simple Boyle-law model?
Reveal response
For fixed amount and temperature, the product PV remains constant.
Mentor evidence conference
Ask Archaemenes to check the model assumptions, unit logic, and physical direction of the result.
Teacher guidance
Foundation: Use a variable organizer before substitution.
Core: Solve and interpret pressure–volume changes.
Extended: Linearize supplied data and evaluate whether it supports the inverse model.