Evaporation
Evaporation is a phase change in which molecules escape from the surface of a liquid and enter the gas phase — and it can happen at any temperature, not just at the boiling point. Unlike boiling, which occurs throughout the bulk of a liquid when it reaches a specific temperature, evaporation is a surface phenomenon driven by the statistical spread of molecular speeds. It is the reason a wet hand feels cool, why sweating cools your body, and why a puddle disappears on a warm day even when the water is nowhere near 100 °C. The key to understanding evaporation lies in the Maxwell–Boltzmann distribution of molecular kinetic energies. In any liquid, molecules are constantly colliding and exchanging energy. At any instant, a small fraction of surface molecules happen to have enough kinetic energy to overcome the intermolecular attractions holding them in the liquid. These high-energy molecules escape into the vapour, leaving behind a liquid whose average kinetic energy — and therefore temperature — is lower. This is the microscopic origin of evaporative cooling. Evaporation rate depends on several measurable factors: temperature (higher temperature → more molecules above the escape threshold), surface area (more surface → more escape opportunities), humidity or vapour pressure above the liquid (if the vapour is already saturated, net evaporation stops), and the strength of intermolecular forces (liquids with weaker intermolecular bonds, like acetone, evaporate faster than water). Understanding these factors has practical applications from industrial drying processes to climate science and human thermoregulation.
- Maxwell–Boltzmann Speed Distribution
- The Energy Barrier: Overcoming Intermolecular Forces
- Why the Remaining Liquid Cools
- Factors Affecting Evaporation Rate
- Evaporation vs. Boiling
Maxwell–Boltzmann Speed Distribution
Molecules in a liquid do not all move at the same speed. Their speeds follow a Maxwell–Boltzmann distribution: most molecules cluster around an average speed, but a tail of the distribution extends to very high speeds. The area under this high-speed tail represents the fraction of molecules energetic enough to escape. As temperature rises, the entire curve shifts to higher speeds and the tail grows larger, so a greater fraction of molecules can evaporate.
The Energy Barrier: Overcoming Intermolecular Forces
A molecule at the liquid surface is attracted downward and sideways by its neighbours but has no neighbours above. To escape, it must do work against these net inward attractive forces. This requires a minimum kinetic energy equal to the binding energy per molecule, roughly related to the molar latent heat of vaporisation: ε_min ≈ L/Nₐ, where L is the specific latent heat (J kg⁻¹) times molar mass, and Nₐ is Avogadro's number. Only molecules whose kinetic energy exceeds ε_min and whose velocity is directed outward can escape.
Why the Remaining Liquid Cools
The escaping molecules are drawn preferentially from the high-energy tail of the distribution — they are the fastest molecules. Removing them lowers the average kinetic energy of the molecules left behind. Since temperature is proportional to average molecular kinetic energy (½m⟨v²⟩ = (3/2)kT for an ideal gas, and analogously for liquids), the liquid's temperature drops. This is not a mysterious effect — it is simply that the highest-energy particles have been selectively removed, which is exactly what lowers the mean.
Factors Affecting Evaporation Rate
Four main factors control how fast a liquid evaporates. (1) Temperature: A higher temperature shifts the Maxwell–Boltzmann curve so more molecules exceed ε_min; rate increases roughly exponentially with T. (2) Surface area: Evaporation is a surface process; doubling the area doubles the number of escape sites. (3) Vapour pressure above the surface: If the air above is already saturated with vapour (relative humidity = 100%), as many molecules re-enter the liquid as leave it — net evaporation is zero. Dry air or wind removes vapour and keeps net evaporation high. (4) Intermolecular forces: Liquids with strong hydrogen bonding (like water, L ≈ 2260 kJ kg⁻¹) evaporate far more slowly than liquids with only weak van der Waals forces (like diethyl ether, L ≈ 360 kJ kg⁻¹) at the same temperature.
Evaporation vs. Boiling
Boiling occurs when the saturated vapour pressure of the liquid equals the external pressure; it happens throughout the liquid and at a fixed temperature for a given pressure. Evaporation occurs only at the surface and at any temperature. The physics, however, is the same escape mechanism — boiling is just the bulk, large-scale version of what evaporation does molecule by molecule at the surface.
The Key Equation
- \dot{m} — Mass evaporation rate (kg s⁻¹): Mass of liquid converted to vapour per unit time.
- A — Surface area (m²): Area of the liquid–air interface exposed to the atmosphere.
- P_{sat}(T) — Saturated vapour pressure (Pa): The vapour pressure at which liquid and vapour are in equilibrium at temperature T; increases steeply with T via the Clausius–Clapeyron relation.
- P_{vapour} — Partial vapour pressure (Pa): The actual partial pressure of the vapour already present in the air above the liquid.
Worked Example
Problem. A runner produces 1.5 kg of sweat during a race. Assuming all of it evaporates, estimate the total thermal energy removed from the runner's body. The specific latent heat of vaporisation of water at body temperature (37 °C) is approximately 2.43 × 10⁶ J kg⁻¹. Then estimate how many degrees Celsius the runner's body temperature would rise if this heat were NOT removed, given the runner's mass is 65 kg and the specific heat capacity of the human body is approximately 3500 J kg⁻¹ K⁻¹.
Answer. Evaporation removes approximately 3.6 MJ of thermal energy, preventing a ~16 °C rise in body temperature.
Origins · 1 minJames Clerk Maxwell and how this was discovered
Maxwell derived the Maxwell–Boltzmann speed distribution (1860), which provides the mathematical foundation for understanding why only a fraction of molecules in a liquid have sufficient kinetic energy to evaporate at a given temperature. His work on the kinetic theory of gases showed that temperature is a statistical property of molecular motion, directly underpinning the explanation of evaporative cooling. Maxwell produced the world's first durable colour photograph in 1861 by combining three black-and-white images taken through red, green, and blue filters — demonstrating his curiosity extended far beyond theoretical physics.
Related Concepts
- Latent Heat of Vaporisation — Evaporation requires energy equal to the specific latent heat per unit mass; this is the energy needed to break intermolecular bonds that evaporating molecules must overcome.
- Saturated Vapour Pressure — Net evaporation stops when the vapour above a liquid reaches its saturated vapour pressure; understanding this concept is essential for predicting evaporation rates and humidity.
- Kinetic Theory of Gases — The Maxwell–Boltzmann speed distribution — central to explaining which molecules escape during evaporation — is derived from kinetic theory.
- Boiling and Condensation — Boiling is the bulk counterpart to surface evaporation; comparing the two clarifies how phase change depends on temperature, pressure, and the same underlying escape mechanism.