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Fridge / Cooler Coleman Cozy

I'm still puzzeling over the idea of adding salt to the ice. Does it really stay cold longer? It seems like if it melts sooner it would warm up quicker. When making ice cream we want the ice to melt and freeze the ice cream sooner but once the ice is melted doesn't it warm up faster?? I sure don't know.
 
Plagiarized explanation :
“To understand freezing point depression, it helps to first understand how melting and freezing work.

Ice absorbs energy (heat) from the environment to break the hydrogen bonds that make it a solid, allowing it to turn into a liquid. In contrast, water releases energy (heat) when it solidifies into ice. Melting is an endothermic process, while freezing is an exothermic process. At the freezing point, these two processes are at equilibrium, so the energy absorbed by water freezing equals the energy released by ice melting. But, when you add salt, you lower the freezing point of the water. Ice melts into water, absorbing heat, but doesn’t re-freeze into ice and release heat. So, the temperature drops.

How does salt lower the freezing point? Salt (NaCl) dissolves in water to form its ions (Na+ and Cl–). The ion particles get between the water molecules and make it harder for them to align to crystallize into ice. This means the temperature has to be colder for the liquid to freeze. Table salt dissolves to form two particles, but some salts dissolve to form more particles and lower the freezing point even more. For example, magnesium chloride (MgCl2) dissolves to form three particles (Mg2+, Cl–, Cl–).

Freezing point depression is an example of a colligative property. A colligative property does not depend on the chemical identity of a substance, but on the number of particles that are formed. Other colligative properties include boiling point elevation and osmotic pressure.”
 
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