Un installateur veut régler le thermostat d'un chauffe-eau...

Un installateur veut régler le thermostat d'un chauffe-eau de telle sorte que celui-ci fournisse de l'eau à $60^{\circ} \mathrm{C}$ mais, pour contrôler cette température, il ne dispose que d'un thermomètre montant à $50^{\circ} \mathrm{C}$ au maximum. Comment pourrait-il procéder (s'il connaissait la thermodynamique...)?

Key Concepts

Thermodynamic Temperature Scale

This concept refers to a temperature measurement system based on universal, reproducible physical phenomena such as phase transitions, rather than the arbitrary scaled measures. It provides a framework that links observed temperatures to absolute quantities, allowing precise calibration and conversion between different measurement ranges—even when the instrument’s native scale, like up to 50°C, does not directly cover the desired application temperature.

Calibration of Thermometers

Calibration is the process of relating a thermometer's readings to known physical fixed points, such as the melting and boiling points of a pure substance, enabling adjustments for accuracy. In contexts where the instrument’s range does not directly include the intended values, thermodynamic principles can be used to shift or interpret readings appropriately, aligning the measured scale with the target temperature through known reference states.

Phase Equilibrium and the Clapeyron Equation

Phase equilibrium involves the balance between different states of matter (such as liquid and vapor) at a given temperature and pressure. The Clapeyron equation mathematically relates these variables, describing how the saturation pressure of a phase transition changes with temperature. By exploiting these relationships, one can determine an unknown temperature indirectly, even if the available instrument does not directly measure that temperature range.

Vapor Pressure Measurement

Vapor pressure measurement utilizes the known thermodynamic relationship between temperature and the pressure exerted by a vapor in equilibrium with its liquid. By measuring the pressure in a controlled system and applying the Clapeyron equation, it is possible to infer the temperature at which the phase equilibrium occurs. This indirect method allows the determination of temperatures that might be outside the direct measurement range of the available thermometer.

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