Why do you need to make an ice water slush mixture (instead of only ice) in order to calibrate your thermometer at 0â°c?

You want an ice water slush because you want a constant repeatable temperature to calibrate your thermometer. If you only had ice, it's possible for the ice to colder than the freezing point of water. The only real limit to how cold you could have the ice is absolute zero (-273 degrees C). So measuring the temperature of ice isn't a reliable reference. On the other side, if you only had water, it could be any temperature between 0°C and 100°C. Once again, not a reliable reference. But if you have a ice water slush, the ice is undergoing a phase change from solid to liquid and the temperature of the slush will remain constant as long as there's still ice melting. And for water, that phase change from solid to liquid occurs at 0°C, so it is a reliable reference you can use to calibrate your thermometer.

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