Extensive vs Intensive Properties: Clear Differences

Thermodynamic properties come in two flavours. Extensive properties depend on how much stuff you have — double the system and they double: mass, volume, internal energy, enthalpy, entropy. Intensive properties do not care about size — temperature, pressure, density and concentration are the same whether you have a spoonful or a swimming pool.

The distinction matters because only intensive properties can describe a material itself (water boils at 100°C at 1 atm, whatever the amount), while extensive properties must be converted to per-mole or per-kg form (molar enthalpy, specific volume) before different systems can be compared.

Key Concepts

• Extensive: mass (kg), volume (m³), moles (mol), internal energy U (J), enthalpy H (J), entropy S (J/K), Gibbs energy G (J), heat capacity C (J/K). All scale with system size and are additive.
• Intensive: temperature (K), pressure (Pa), density (kg/m³), concentration (mol/L), refractive index, boiling point. Independent of amount; not additive.
• Molar properties: extensive ÷ moles — e.g. molar enthalpy (J/mol), molar volume (m³/mol). The chemist's favourite intensive form.
• Additivity test: split a system in two — extensive properties split with it, intensive ones stay the same in each half.

How It Works

1. Take 2 kg of water at 25°C. Mass (2 kg), volume (~2 L) and total internal energy are extensive.
2. Pour half into another beaker: each half has 1 kg, ~1 L, and half the internal energy — the extensive values split.
3. But each half is still at 25°C with density 1000 kg/m³ — temperature and density are intensive and unchanged.
4. To tabulate energy data usefully, divide by amount: molar enthalpy of vaporisation of water is 40.7 kJ/mol at 100°C — an intensive value valid for any quantity.
5. In calculations, convert intensive table data back to extensive (multiply by moles or mass) for your actual system size.

Worked Example

How much heat is needed to warm 500 g of water from 20°C to 80°C? Specific heat capacity of water c = 4.18 J/g·K (intensive).

1. Temperature change ΔT = 80 − 20 = 60 K (intensive — same for any amount of water).
2. Convert to extensive heat: q = m c ΔT = 500 g × 4.18 J/g·K × 60 K = 125,400 J ≈ 125 kJ.
3. Double the water to 1000 g and q doubles to ~251 kJ — heat is extensive.
4. The specific heat capacity 4.18 J/g·K never changes — that is what makes it intensive and tabulate-able.
5. Check with molar form: 500 g = 27.75 mol; molar heat capacity = 4.18 × 18.0 = 75.2 J/mol·K; q = 27.75 × 75.2 × 60 = 125,208 J. Same answer, as it must be.

Common Misconceptions

• "Density depends on how much you have." No — doubling the mass doubles the volume too, so mass/volume stays fixed. That constancy is exactly why density identifies substances.
• "Enthalpy values in tables can be used directly." Tables list molar enthalpies (kJ/mol, intensive). You must multiply by your actual moles to get the extensive ΔH of your reaction — forgetting this factor is the commonest thermochemistry error.

Real-World Applications

• Engineering tables: steam tables list specific enthalpy and specific volume (intensive) so one table serves power plants of any size.
• Chemistry data books: standard molar enthalpies of formation (kJ/mol) let chemists compute ΔH for any reaction scale via Hess's law.
• Calorimetry: measured heat (extensive, depends on sample mass) is always divided by moles to report comparable molar quantities.

In short, extensive properties scale with amount (mass, volume, energy) while intensive ones do not (temperature, pressure, density).