Why water boils at a lower temperature on top of Everest
In short: At high altitudes, the atmosphere thins, and the physics of phase changes shift. The Clausius–Clapeyron relation explains why your tea won't reach a rolling boil on a mountain peak, revealing a fundamental link between pressure, temperature, and the latent heat of vaporization.
The Clausius–Clapeyron relation describes how the pressure at which a substance undergoes a phase transition—like water turning into steam—varies with temperature. It is a cornerstone of chemical thermodynamics, specifically defining the slope of the 'coexistence curve' on a pressure-temperature (P–T) diagram. Although Rudolf Clausius and Benoît Paul Émile Clapeyron provided the namesake, Sadi Carnot first formulated the core principles during 1824, yet the work stayed mostly overlooked before being found again many years on.
The mechanism relies on the balance of energy during a phase change. When liquid water turns to steam at a constant temperature, it absorbs the 'latent heat of vaporization' (λ). For one mole of water at 100 °C, this value is 40.65 kilojoules per mole. Because the volume of steam (30.143 litres) is vastly larger than the volume of liquid water (0.0188 litre), the first law of thermodynamics shows that the change in internal energy is tied to both this latent heat and the work done by the expanding gas. By mathematically relating these variables, scientists can predict the exact boiling point at any given pressure.
In practical terms, this equation explains why atmospheric pressure dictates boiling points. At the summit of Mount Everest, the atmospheric pressure is approximately 30 percent of its sea-level value. Applying the Clausius–Clapeyron equation with the ideal gas constant (R = 8.3145 J/K) reveals that water boils at about 342 K (69 °C) there. This demonstrates the 'sweeping generality' of thermodynamics: the laws governing these transitions are independent of the microscopic structure of matter, providing universal predictions for how substances behave across the globe.
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Sources
- Summary by Intellect · source: Thermodynamics - Clausius-Clapeyron, Heat, Pressure | Britannica
- Also: Clausius–Clapeyron relation
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