8.3Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
Section · module m68751
What this needs
Learn these first — this section will not make sense without them.
The combined-gas-law worked example (scuba tank problem) never rearranges P1V1/T1 = P2V2/T2 symbolically before substituting — it plugs all four known numbers straight into the unrearranged equation, (153 atm)(13.2 L)/(300 K) = (3.13 atm)(V2)/(310 K), and only then isolates the single remaining unknown V2 from that fully numeric equation, i.e. a rational equation with the unknown inside a quotient — the same 'clear the equation, isolate the letter, but with numbers already in place' move as algebra section 2.3's rational-equation content, and the reliable error is forgetting to convert both temperatures to kelvin before cross-multiplying.
The single-state ideal-gas-law worked example (methane volume problem) takes the opposite order: PV = nRT is rearranged to V = nRT/P entirely in symbols before a single number is substituted ('We must rearrange PV = nRT to solve for V'), then n, T, and P are separately converted to the right units and plugged into the already-isolated formula — the solve-a-formula-for-a-specified-variable move, done up front rather than after the numbers are in place.
What this touches
Algebra that turns up here. Not a blocker, but this is where you will see it used.
- Applies5.9Modeling Using Variation
Amontons's law (P∝T), Charles's law (V∝T), and Boyle's law (P∝1/V) are each stated in the text as explicit proportionalities before being converted to the P₁/T₁=P₂/T₂ or P₁V₁=P₂V₂ working forms — the same direct- and inverse-variation vocabulary as a variation-modeling problem, just introduced under the historical names of the laws.