It depends on what you mean by “get colder faster.”
Heat transfer rates are a function of a difference in temperature, but this rate is at a given moment in time. Thus, as the items approach each other in temperature, the actual rate of heat transfer decreases, and thus the rate of change of temperature also decreases.
So, strictly speaking, the item in the fridge at 30C will lose heat more rapidly than the item at 15C at first, but if your end goal is to reach a certain *particular* temperature (e.g. 5C), the object at 15C will still get there first.
It depends, but the surprising answer is for liquids, Yes, probably.
Hot water will freeze faster than cold water when cooled.
The basic reason is because heat causes liquids to to move around in a process called “convection” (the same reason hot air rises and cold air sinks, but now imagine that rising and sinking occurring in a circuit and constantly moving around and around). This convection essentially keeps the heat on “outside” of the water and makes it easier to to cool down.
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