Eli5 – would it take more time/energy to boil a pint of frozen water or freeze a pint of boiling water?
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Assuming the freezing temperature was the same, the amount of time would be the same. What I mean by assuming the freezing temperatures are the same is if we start with 100g of water at 0F, and heat it to 212F and compare it to another 100g of water that is 212F and cool it down to 0F, both would take the same time and energy.
There is a concept called heat of fusion, which says how much energy is needed to move from solid to a liquid, and it is equal and opposite to the heat of solidification, which is the amount of energy to go from liquid to a solid.
The total energy to _move_ is the same. Problem is cooling is much harder to do efficiently. To cool, you use electro-mechanical force to shove a gas between regions of high to low pressure (or tightly compressed to big volume; as the gas rapidly expands to fill the increased volume it draws thermal energy from the surroundings.) But the motors and pumps to do this are not perfectly efficient – some energy will be lost as waste heat from the mechanical bits, the motors/pumps etc. Meanwhile, if you use appropriate insulation you can extract nearly 100% of the input energy from an electric heating element. Thus to move the same amount of thermal energy either into or out of the water, its much more efficient to move it INTO the water with a heater than remove it using less efficient refrigeration.
And time is too variable – if you have a large enough heating element you can flash vaporize a pint of water instantly. Likewise if you had a super large chiller setup you could flash freeze a pint of water relatively quickly (not like, instantly, but within a minute or two.)
So this isn’t a great question. It takes energy to boil, it does not take energy to freeze
You remove energy to freeze, not add. The amount of energy to add and the amount of energy to remove are equal in your scenario, but going in opposite directions.
Heat transfer is generally proportional to temperature difference and surface area. Assuming the heat transfer is equal in both scenarios then time will be equal (ignoring the fact that one way may be slightly off depending on how if you count the phase change or not). However, it’s significantly easier to create a positive temperature differential to add heat than it is to create a negative temperature differential to remove. So, using conventional methods like a standard kettle & freezer the kettle will easily boil the frozen water before the freezer can freeze anything.
To illustrate, a freezer might run at -20C (and probably not even that cold). So 20 below freezing. A gas hob or electric kettle can easily reach several hundred C, so several hundred above boiling. A bigger temperature difference gives bigger heat transfer, and faster results.
Assuming the mass of water is the same in both scenarios (density of water changes with different phases), the amount of energy is the same. However, the time it’ll take to get frozen water to boiling is dependent on how quickly you can add energy to it (heating power), while freezing boiling water depends on how quick you can take away the energy (cooling power).
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