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I know how to use a thermometer to determine the pressure (the Clapeyron-Clausius equation) or to conduct an experiment with heating water to a boil, and look at the table of the dependence of the boiling point on the pressure, but how to use a barometer to determine the temperature?

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The density of mercury will change with an increase or decrease in temperature, so reading must be adjusted for the temperature of the instrument. For this purpose, a mercury thermometer is usually mounted on the instrument. Temperature compensation of an aneroid barometer is accomplished by including a bi-metal element in the mechanical linkages. Aneroid barometers sold for domestic use typically have no compensation under the assumption that they will be used within a controlled room temperature range.

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