Паровий Тиск та Кипіння: Рівняння Клапейрона-Клара

The Nature of Vapor Pressure

Vapor pressure refers to the pressure exerted by the vapor phase of a substance in equilibrium with its liquid or solid phase. This pressure arises from the kinetic energy of the molecules within the substance, which causes them to escape into the gaseous state. The higher the temperature, the greater the average kinetic energy of the molecules and, consequently, the higher the vapor pressure.

Equilibrium is established when the rate at which molecules evaporate from the liquid surface equals the rate at which vapor molecules condense back into the liquid. At this point, the partial pressure of the vapor in equilibrium with the liquid is termed the equilibrium vapor pressure. It’s important to note that this pressure changes with temperature; increasing the temperature increases the vapor pressure.

Phase Changes: Liquid to Gas

Phase changes occur when a substance transitions between different states. Specifically, liquid-to-gas phase change (boiling) is driven by the system seeking to minimize its energy and achieve equilibrium with the surrounding environment.

Boiling occurs when the vapor pressure of the liquid equals the external pressure acting upon it. This means that at this specific temperature, bubbles of gas form within the liquid and rise to the surface. The bubble formation isn't simply due to evaporation from a surface; instead, it’s a result of the liquid transitioning directly into the gaseous phase.

The boiling point of a substance is defined as the temperature at which its vapor pressure equals the external pressure. For example, water boils at 100°C (212°F) at standard atmospheric pressure (1 atmosphere). However, if the external pressure changes – for instance, at higher altitudes where the air pressure is lower – the boiling point will also change.

The Clausius-Clapeyron equation

The Clausius-Clapeyron relation connects how a liquid’s vapor pressure changes with temperature to its molar enthalpy of vaporization, treating the vapor as an ideal gas over the liquid-vapor coexistence line:

dP/dT = ΔH_vap / (T ΔV) (Clapeyron equation)

Integrated (ideal-gas, ΔH_vap ~ constant over a small range): ln(P₂/P₁) = -(ΔH_vap / R) · (1/T₂ - 1/T₁) Given a liquid’s vapor pressure at one known temperature and its enthalpy of vaporization, this lets you predict its vapor pressure — and therefore its boiling point — at any other temperature, or under any other external pressure.

dP/dT = ΔH_vap / (T ΔV)     (Clapeyron equation)

Integrated (ideal-gas, ΔH_vap ~ constant over a small range):
  ln(P₂/P₁) = -(ΔH_vap / R) · (1/T₂ - 1/T₁)

Why altitude changes the boiling point

Atmospheric pressure falls steadily with altitude, so a liquid needs a lower vapor pressure — reached at a lower temperature — to match the surrounding air pressure and start boiling. At roughly 3,000 metres, water can boil at around 90°C instead of the sea-level 100°C, which is exactly why food takes noticeably longer to cook properly at high altitude.

P_ext < 1 atm   →   lower boiling point   (high altitude)
P_ext > 1 atm   →   higher boiling point  (pressure cooker)

Pressure cookers do the opposite

A sealed pressure cooker lets internal pressure climb well above 1 atmosphere as steam accumulates with nowhere to escape. Because boiling still requires vapor pressure to match the surrounding pressure, water inside must reach a higher temperature — commonly around 120°C — before it can boil. Cooking at that elevated temperature speeds up the underlying heat-transfer and chemical processes involved in cooking, cutting typical cooking times substantially.

Frequently asked questions

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