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Measurement · PhysicsRadiant flux, intensity, irradiance, exitance and radiance

Optical power, directional power and surface densities are different quantities.

DefinitionMeasurement · PhysicsPhotometric weighting, lumen, candela, lux and luminance

Photometry weights radiation with a specified standard visual response.

DefinitionMeasurementWriting SI quantities and unit symbols

Symbol form, spacing and parentheses preserve the meaning of reported quantities.

DefinitionMeasurementGram prefixes and the kilogram exception

Mass prefixes attach to gram even though kilogram is the SI base unit.

DefinitionMeasurementRounding a result with its uncertainty

Report useful digits without treating extra digits as proof of accuracy.

MethodMeasurement · Physics · ChemistryCommon non-SI units and exact SI conversions

Common non-SI unit names require their correct SI scale factors.

DefinitionPhysics · ChemistryGas pressure as molecular momentum transfer

Molecular collisions link macroscopic pressure to random translational motion.

ModelChemistry · PhysicsOrdinary aggregate states and bulk behavior

Solid, liquid and gas describe bulk behavior rather than chemical identity.

ModelChemistryInferring empirical and molecular formulas from composition

Element mass ratios become atom ratios through molar masses, with uncertainty and sample identity retained.

MethodChemistryLewis structures and valence-electron accounting

A Lewis diagram accounts for bonding and nonbonding valence electrons in a specified connectivity.

MethodChemistryElectron-domain geometry and molecular shape

VSEPR distinguishes the arrangement of electron regions from the positions of atoms.

ModelChemistryElectronegativity, bond polarity and molecular polarity

Polar bonds can cancel in a molecule; molecular geometry matters.

ModelChemistrySolutions, solutes, solvents and solvation

Dissolution disperses specified molecular or ionic species in a solvent.

DefinitionChemistrySolubility, saturation and supersaturation

A saturation limit is an equilibrium property under specified conditions, not a synonym for concentration.

DefinitionChemistryFiltration separates retained solids from a fluid

Ordinary filtration separates undissolved particles; dissolved species can remain in the filtrate.

MethodChemistryDistillation and vapor–liquid composition

Distillation uses vapor–liquid partitioning and condensation, with a limit at an azeotrope.

MethodBiologyGene, allele, genotype and phenotype

Genomic sequence variants and observable traits describe different levels of biological information.

DefinitionBiology · ChemistryEnzyme substrates, active sites and induced fit

Substrate recognition and catalysis depend on a dynamic molecular environment.

ModelBiology · ChemistryMonomers, polymers and hydrolysis

Covalent subunit linkage and water-assisted cleavage explain biological polymer structure.

DefinitionBiology · ChemistrySugars, glycosidic linkages and polysaccharides

Sugar connectivity distinguishes energy-storage and structural polysaccharides.

DefinitionBiology · ChemistryFatty acids, storage lipids and membrane lipids

Lipids include several architectures rather than one repeating-monomer polymer class.

DefinitionBiology · ChemistryAmino-acid residues and peptide linkages

The peptide backbone and variable side chains are different parts of protein structure.

DefinitionBiology · ChemistryNucleotides and DNA/RNA backbone polarity

Bases carry sequence information on a chemically directional sugar–phosphate backbone.

DefinitionBiologyCell membrane, cell wall, cytosol and compartments

A cell's boundary, fluid interior and specialized structures have different roles.

DefinitionEarth & cosmos · MeasurementEarthquake location, source magnitude and local intensity

A source location or magnitude does not describe the shaking experienced at every site.

DefinitionEarth & cosmosAtmospheric composition and thermal layers

Composition and temperature structure describe different features of Earth's atmosphere.

ModelEarth & cosmosDrainage basins, outlets and water divides

Surface drainage boundaries depend on the chosen outlet and need not bound groundwater flow.

DefinitionEarth & cosmosThe celestial sphere and the observer's sky

A sky direction is an angular observation, not an object's three-dimensional distance.

ModelEarth & cosmos · MeasurementRight ascension, declination and reference epochs

Celestial angular coordinates require a declared reference system and date conventions.

Definition
ModelSource checked

Gas pressure as molecular momentum transfer

PhysicsChemistry

Molecular collisions link macroscopic pressure to random translational motion.

Key knowledge

For a dilute classical ideal gas with isotropic molecular velocities in its rest frame, elastic wall collisions transfer momentum and give pV=Nm⟨v²⟩/3. Combining this with pV=Nk_BT gives mean translational kinetic energy m⟨v²⟩/2=3k_BT/2 and rms speed √⟨v²⟩=√(3k_BT/m). The rms speed is distinct from the mean speed and the net drift velocity.

Values and equations

pV=Nm⟨v²⟩/3=Nk_BT; ⟨K_trans⟩=m⟨v²⟩/2=3k_BT/2; v_rms=√⟨v²⟩=√(3k_BT/m)

p
Equilibrium gas pressure Pa
V
Gas volume m³
N
Number of identical gas particles 1
m
Mass of one gas particle kg
v,v_rms
Particle speed relative to the gas rest frame and root-mean-square speed m s⁻¹
⟨v²⟩
Ensemble mean squared particle speed m² s⁻²
⟨K_trans⟩
Mean translational kinetic energy per particle J
k_B
Boltzmann constant J K⁻¹
T
Absolute equilibrium gas temperature K

Conditions and scope

  • Use N>0 identical particles of mass m>0 in volume V>0, at uniform equilibrium temperature T>0; translational velocities are relative to the gas rest frame.
  • The collision derivation assumes an ideal dilute gas, isotropic motion, elastic walls and negligible interparticle potential/volume corrections.
  • The translational energy is not the complete internal energy of a molecule with accessible rotational, vibrational or electronic degrees of freedom.
Sources · 2

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics Volume 2, 2-2-pressure-temperature-and-rms-speedSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University (2016)Textbook chapteropenstax.orgRead source
  2. Kinetic Theory · Physics (2026–27 reprint)National Council of Educational Research and Training (NCERT)Textbook chapter · PDFncert.nic.inRead source

Evidence and review

Elastic wall momentum transfer and an isotropic dilute ideal-gas velocity distribution give the pressure–mean-square-speed relation.

2026-10-10 · Independent Chemistry, Biology and Earth/Cosmos editor (AI editorial review). Source checks and independent AI editorial review of compact reference claims, equations, units, conditions and conceptual mappings. This is not human specialist certification, laboratory accreditation, whole-book verification, or a claim that all possible foundational knowledge is present.

Foundational review

2026-10-10 · Independent AI editorial inspection of this new compact reference entry, its equations, applicability, sources and knowledge connections.

Sources from other places

Agreement within this scope

The isotropic classical ideal gas connects pressure with mean squared random speed and translational energy with 3kT/2.

Root mean square speed differs from mean speed and drift velocity; molecular internal modes add separate degrees of freedom.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–4 of 4 relationships

Scientific relationships · 4 / 4

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Derived from
    Relationship sources · 1

    Linked statements

    • For a dilute classical ideal gas with isotropic molecular velocities in its rest frame, elastic wall collisions transfer momentum and give pV=Nm⟨v²⟩/3. Combining this with pV=Nk_BT gives mean translational kinetic energy m⟨v²⟩/2=3k_BT/2 and rms speed √⟨v²⟩=√(3k_BT/m). The rms speed is distinct from the mean speed and the net drift velocity.

    The idealized wall pressure follows time-averaged momentum transfer in elastic molecular collisions.

  2. Related to
    Relationship sources · 1

    Linked statements

    • For a dilute classical ideal gas with isotropic molecular velocities in its rest frame, elastic wall collisions transfer momentum and give pV=Nm⟨v²⟩/3. Combining this with pV=Nk_BT gives mean translational kinetic energy m⟨v²⟩/2=3k_BT/2 and rms speed √⟨v²⟩=√(3k_BT/m). The rms speed is distinct from the mean speed and the net drift velocity.

    The molecular count form pV=Nk_BT is the existing amount-of-substance ideal-gas relation with n=N/N_A and R=N_Ak_B.

  3. Related to
    Relationship sources · 1

    Linked statements

    • For a dilute classical ideal gas with isotropic molecular velocities in its rest frame, elastic wall collisions transfer momentum and give pV=Nm⟨v²⟩/3. Combining this with pV=Nk_BT gives mean translational kinetic energy m⟨v²⟩/2=3k_BT/2 and rms speed √⟨v²⟩=√(3k_BT/m). The rms speed is distinct from the mean speed and the net drift velocity.

    The existing distribution gives the same equilibrium mean kinetic energy; the pressure derivation additionally uses wall momentum transfer.

  4. Uses definition
    Relationship sources · 1

    Linked statements

    • For a dilute classical ideal gas with isotropic molecular velocities in its rest frame, elastic wall collisions transfer momentum and give pV=Nm⟨v²⟩/3. Combining this with pV=Nk_BT gives mean translational kinetic energy m⟨v²⟩/2=3k_BT/2 and rms speed √⟨v²⟩=√(3k_BT/m). The rms speed is distinct from the mean speed and the net drift velocity.

    Uses the exactly defined Boltzmann constant in the equilibrium relation.

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