Top tips for keeping your fridge cold

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Ice will stay at 0°c for hours though while it melts, all the time absorbing heat.

Whereas a volume of salt water will just continue warming up past 0°c

I remember the lecturer saying something about the large amount of heat it takes to melt ice..

You're right, freezing water into ice is the best way to keep things at about 0 deg C. A large amount of heat is required just to melt ice - enough to raise the temperature of the same weight of liquid water by nearly 80 deg C. But if you want to store things at much below zero then salt water might be better.