Couze The water in the buket has some energy (tempreture) it is absorbed by the water and the ice melts this way water cools...now if you consider the ice outside the bucket water will no longer be in tuch with ice ,since energy of water since must be absorbed the ice first need to bring down the bucket's temp such that it must be less then the temp of water then the energy of water can be absorbed by the bucket and to the ice and surrounding (if its cooler)..
MORE GENRALY......
WITH OUT EXTERNAL AID TEMPERATURE FLOWS FROM HIGHER POTENTIAL TO LOWER POTENTIAL ALWAYS!
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