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Concept · Thermodynamics
Kinetic theory & temperature
matter as molecules, Brownian motion & diffusion as evidence, temperature as a measure of AVERAGE molecular KE (Kelvin scale, t=T-273.15), average translational KE E=(3/2)kT, average vs individual molecular speeds, molecule counting via NA (N=(m/M)NA), oil-film monolayer estimate
Switches you to Physics
Named traps
13 ways this goes wrong.
Each is a named misconception the questions are built to catch. Open one for the move that tempts, and the fix.
- Average KE proportional to Celsius tempUses Celsius rather than absolute (Kelvin) temperature when relating average molecular KE to temperature, so doubling Celsius is read as doubling KE.→
- Average speed equals individual speedTreats the average molecular speed as the speed of every individual molecule, ignoring the distribution of speeds.→
- Brownian motion blamed on currentsAttributes Brownian jiggling to air/convection currents or vibration rather than to unbalanced molecular collisions.→
- Brownian particle is a moleculeInterprets the visible Brownian particle itself as a molecule rather than as a larger particle revealing molecular bombardment.→
- E=(3/2)kT fed Celsius temperatureSubstitutes a Celsius temperature into E=(3/2)kT, or drops the 3/2 factor, when finding average translational KE.→
- Mass ignored for molecular speedAssumes molecules of different mass have the same speed at the same temperature, ignoring that average speed depends on molecular mass.→
- Molar mass units mismatchedMixes grams and kilograms (or molar mass vs molecular mass) in N=(m/M)NA, giving a count off by 1000.→
- Molecular speed unaffected by TAssumes molecular speeds do not change with temperature, or that every molecule moves at the same single speed.→
- N=(m/M)NA skippedReports the number of moles or the mass as the number of molecules, forgetting to multiply by Avogadro's number NA.→
- Oil film not treated as monolayerForgets that the oil-film estimate assumes a single-molecule-thick layer, so diameter = volume/area is not applied.→
- Oil-film thickness formula invertedComputes molecular diameter as area/volume instead of volume/area in the oil-film monolayer estimate.→
- Temperature as total KELinks temperature to the total molecular kinetic energy of the sample rather than to the average per molecule.→
- k Coulomb constant used for kBPlugs the Coulomb constant k (~9 × 109) into E=(3/2)kT instead of the Boltzmann constant kB (~1.38 × 10-23), confusing the two symbols.→
Key formulas
No formula sheet is matched to this concept yet. Work it from first principles, and watch the traps.
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPhysics 2 breadthMechanics foundations