Evaporation & Cooling

Evaporation is a surface phenomenon in which molecules at the liquid surface escape into the vapour phase without the bulk liquid reaching its boiling point. Unlike boiling, which occurs throughout the entire volume of a liquid at a fixed temperature, evaporation can occur at any temperature as long as the surface molecules possess sufficient kinetic energy to overcome the intermolecular attractive forces holding them in the liquid state. This distinction is critical: a puddle disappears on a cool day not because the water boils, but because its fastest-moving surface molecules continuously escape into the air. The escaping molecules carry away above-average kinetic energy, leaving behind molecules with a lower average kinetic energy. Because temperature is a measure of the average kinetic energy of particles, the remaining liquid cools down. This cooling effect underpins many biological and technological processes — from sweating in mammals to refrigeration cycles and the operation of evaporative coolers. Water's relatively high enthalpy of vaporization ( $\Delta H_{\text{vap}} = 44.0$ kJ/mol at 25 °C) makes it an exceptionally effective cooling agent. Five major factors govern the rate of evaporation: temperature, surface area, humidity (concentration of vapour above the liquid), wind speed or air movement, and the nature of the liquid itself (particularly its intermolecular forces and vapour pressure). Understanding these factors allows chemists and engineers to control evaporation for practical purposes, from drying industrial coatings to designing efficient heat exchangers and predicting weather patterns.

Key takeaways

Kinetic Energy Distribution in a Liquid
Why Evaporation Is a Surface Phenomenon
The Cooling Effect Explained
Factors Affecting Rate of Evaporation
Vapour Pressure and Dynamic Equilibrium

Kinetic Energy Distribution in a Liquid

Molecules in a liquid do not all move at the same speed. Their speeds follow a Maxwell–Boltzmann distribution — a bell-shaped curve skewed to the right. At any given temperature, a small fraction of surface molecules have enough kinetic energy to overcome the net inward attractive forces (London dispersion, dipole–dipole, or hydrogen bonding). Only these high-energy surface molecules escape. The minimum energy required equals the enthalpy of vaporization per molecule, ΔH_vap/Nₐ, where Nₐ is Avogadro's number.

Why Evaporation Is a Surface Phenomenon

Interior molecules are surrounded on all sides by neighbouring molecules, so intermolecular attractions pull equally in every direction — the net force is zero. Surface molecules are attracted inward and sideways but have no neighbours above them in the vapour phase. Consequently, only surface molecules experience the net inward pull they must overcome to escape. This is why evaporation rate is proportional to the exposed surface area of the liquid, not to its volume.

The Cooling Effect Explained

When the fastest molecules (highest KE) escape, the average KE of those remaining decreases. Since temperature ∝ average KE, the liquid temperature drops. Quantitatively, the heat removed per mole of liquid evaporated equals ΔH_vap. For water at skin temperature (~33 °C), ΔH_vap ≈ 43.5 kJ/mol. Evaporating just 1 g of sweat (≈ 0.0555 mol) absorbs 43.5 × 0.0555 ≈ 2.41 kJ of heat from the body — enough to cool 100 mL of water by approximately 5.8 °C.

Factors Affecting Rate of Evaporation

1. Temperature: Higher T shifts the Maxwell–Boltzmann curve right, giving more molecules the energy to escape. 2. Surface Area: More surface molecules are exposed, so the escape rate increases proportionally. 3. Humidity / Vapour Pressure: If the air above the liquid is already saturated with vapour (relative humidity = 100%), the rate of molecules re-entering the liquid equals the escape rate — net evaporation stops. Lower humidity = faster evaporation. 4. Wind / Air Movement: Removes vapour molecules from above the surface, preventing re-condensation and maintaining a concentration gradient that drives net evaporation. 5. Nature of Liquid: Liquids with weak intermolecular forces (e.g., diethyl ether, C₂H₅OC₂H₅) have high vapour pressures and evaporate rapidly; those with strong hydrogen bonding (e.g., water, glycerol) evaporate slowly.

Vapour Pressure and Dynamic Equilibrium

In a closed container, evaporation does not stop; instead, vapour molecules also condense back. When the rate of evaporation equals the rate of condensation, a dynamic equilibrium is established and the pressure exerted by the vapour is called the saturated vapour pressure (SVP). SVP depends only on temperature and the nature of the liquid (not volume or amount of liquid present). The Clausius–Clapeyron equation describes how SVP changes with temperature: ln(P₂/P₁) = −ΔH_vap/R × (1/T₂ − 1/T₁), where R = 8.314 J mol⁻¹ K⁻¹.

The Key Equation

\ln\!\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{\text{vap}}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)

P_1,\, P_2 — Saturated vapour pressure (Pa or atm): The equilibrium vapour pressure of the liquid at temperatures T₁ and T₂ respectively.
\Delta H_{\text{vap}} — Enthalpy of vaporization (J mol⁻¹): Energy required to convert one mole of liquid to vapour at constant pressure; for water ≈ 44,000 J mol⁻¹ at 25 °C.
R — Universal gas constant (J mol⁻¹ K⁻¹): R = 8.314 J mol⁻¹ K⁻¹; relates energy scale to temperature in thermodynamic equations.
T_1,\, T_2 — Absolute temperature (K): Temperatures in Kelvin (K = °C + 273.15) at which the vapour pressures P₁ and P₂ are measured.

Worked Example

Problem. The saturated vapour pressure of water is 3.17 kPa at 25 °C (298 K). Using ΔH_vap = 44,000 J mol⁻¹ and R = 8.314 J mol⁻¹ K⁻¹, calculate the saturated vapour pressure of water at 50 °C (323 K).

P_2 \approx 12.6 \text{ kPa}

Answer. The saturated vapour pressure of water at 50 °C is approximately 12.6 kPa.

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Diagram

Origins · 1 minRudolf Clausius and how this was discovered

Rudolf Clausius

1822–1888 · German

Rudolf Clausius was a pioneering thermodynamicist who formulated the Clausius–Clapeyron equation (building on Émile Clapeyron's earlier work) describing how vapour pressure depends on temperature via the enthalpy of vaporization. He also gave the first clear mathematical statement of the Second Law of Thermodynamics and introduced the concept of entropy (from Greek 'trope', meaning transformation). His kinetic theory work directly underpins our modern understanding of why evaporation occurs and what drives the cooling effect. Clausius coined the word 'entropy' in 1865, deliberately choosing a Greek-derived term to parallel 'energy', saying he wanted the two most important quantities in physics to have names from the same language.

States of Matter — Evaporation is a liquid-to-gas phase transition; understanding the arrangement and energy of particles in different states is a prerequisite for explaining why only surface molecules can escape.
Intermolecular Forces — The strength of hydrogen bonding, dipole–dipole, and London dispersion forces directly determines a liquid's enthalpy of vaporization and therefore its evaporation rate and cooling power.
Enthalpy and Thermochemistry — The cooling effect is quantified through ΔH_vap; understanding enthalpy as heat flow at constant pressure is essential for calculating how much heat is absorbed during evaporation.
Kinetic Molecular Theory — The Maxwell–Boltzmann distribution of molecular speeds explains which molecules can escape during evaporation and why temperature affects the evaporation rate.
Vapour Pressure and Boiling Point — Saturated vapour pressure is the equilibrium outcome of evaporation in a closed system; boiling occurs when vapour pressure equals external pressure, linking evaporation to the concept of boiling point.