Particles in a fluid will increase its boiling point, and decrease its freezing point. The more particles, the more change from normal. You can actually use math to figure this out precisely.
Anyway salt dissolves easily in water and adds lots of particles. This makes the freezing point decrease, making it melt. In a traditional home ice cream maker the effect of melting ice (solid to liquid) absorbs a lot of energy (heat) from the ice cream mix making it cold. The ice cream has less particles compared to the salty mix, so it freezes while the salty mix is like a slushy.
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