8.6The Kinetic-Molecular Theory
Section · module m68758
What this needs
Learn these first — this section will not make sense without them.
u_rms=√(3RT/M) is a square root of a quotient, and deriving Graham's law from it means squaring both sides to isolate M (M=3RT/u²_rms) — the same radical-manipulation skill §8.5 needs, now embedded inside a formula with three other variables.
What this touches
Algebra that turns up here. Not a blocker, but this is where you will see it used.
- Applies2.4Models and Applications
KE_avg = (1/2)Mu_rms^2 and KE_avg = (3/2)RT are set equal and solved for u_rms — u_rms = sqrt(3RT/M) — entirely in the section's own exposition, in symbols, before the worked example ever introduces a number; by the time the student reaches 'Calculation of u_rms' they are handed the already-rearranged formula and only ever substitute into it. The literal-equation isolate-a-variable step is performed by the text rather than required of the reader, but the resulting formula is exactly a solve-for-a-specified-variable result, and the section leans on the reader being able to follow that derivation to trust the formula rather than merely memorize it.