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Diluting concentrated ethanol with water is exothermic. Diluting 95% refined spirit into 40% vodka makes the resulting product definitely warm. Dilution of 60% absinthe with water that is cool, but warmer than "nearly freezing" results in a lukewarm, unappetizing drink. I haven't noticed the effect when diluting weaker alcohols though.

Is there a threshold of concentration where further dilution of water-ethanol mix doesn't produce heat? Or is it merely an asymptotic relation, where at lower concentrations the effect becomes hard to notice?

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Mixing ethanol and water is exothermic all over the range at about room temperature. Data are available, e.g., here excess enthalpy ethanol-water

However, at relatively high temperature and at least around azeotropic composition, the mixing should become endothermic otherwise the ethanol-water azeotrope should boil at higher temperature instead of having Bp of 78.1 °C.

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