Well of course without specific information we can't calculate an actual time. Even the shape of the chunk of hail would be a factor (because of the effect of surface area). For the time being I would assume as you did that there is no loss of ice all the way home, until it is placed in the freezer. We also need to know the temperature of the freezer, but I guess we can assume 0°C for simplicity. I've noticed that ice cubes in a frost-free freezer slowly disappear if they are just left in the freezer for a long time. During the defrost cycle they may melt on the surface just slightly and slowly evaporate that way, or if no actual melting occurs the ice may just slowly sublime. Either way, you are converting ice at 0°C to water vapor at 0°C overall.
Or, the problem could be asking how long it will take the piece of hail simply to melt when it asks how long it will "last", in which case we would have a shorter calculation for H2O (s, 0°) --> H2O (l, 0°). In this case we don't have to consider the conversion to vapor, H2O (l, 0°) --> H2O (g, 0°).
Using the heat of fusion of ice (6.01 kJ/mol) you can calculate the joules of heat needed for melting the moles of ice in the piece of hail at 0°C. There is no temperature change here. If you want to also include the heat needed to evaporate the liquid, add moles of ice X 44.01 kJ/mol (this number is the standard DH° for the process H2O(l) --> H2O (g) which should be about right at 0° also).
Now you have a value for the total heat, but what about the time? That depends on lots of things, such as how well the ice contacts the defroster coils in the freezer, if the freezer is "standard" or "automatic" frost-free, how long the defroster is on and off (automatic defrost), and the wattage of the defroster. Typical defroster times are 20 minutes every six hours.
Again for simplicity I guess you could assume that all of the heat from the defroster coils are transferred to the ice during the defrosting cycle (I'm assuming automatic defrost). If you know how many joules of heat are transferred to the ice in each 20 minute heating period, you can calculate the total time it would take to melt, or melt and vaporize, the ice.
This amount of heat would be the watts of power used by the defroster coils times the time in seconds (20 min = 1200 s). A watt is a joule per second, J/s. The defroster coils use perhaps 350 watts of power (estimated from here). The joules of heat transferred to the ice would be (350 J/s)(1200 s) = 420,000 J or 420 kJ. From this, calculate the number of 20 min heating periods needed to evaporate all the ice and add the times between the periods when the defroster is off (say, cycles of 6 hours off, 20 min on) and that should give you the total time for your precious chunk of hail to disappear! This is definitely a "
" kind of problem! (And a "
" analysis! Hope it gets you on the right track.)
Steve
How frost-free freezers work -
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