Two ice cubes of 50 g each (so 100 g of ice) at -15 degC are dropped into 250 g of water at 25 degC. Using specific heat of ice = 0.5 cal/g/degC and latent heat of fusion L = 80 cal/g, find the final temperature and the final amounts of water and ice.

0 degC, 300 g water and 0 g ice
0 degC, 250 g water and 50 g ice
0 degC, 200 g water and 100 g ice
25 degC, 300 g water and 0 g ice

Correct answer: 0 degC, 250 g water and 50 g ice

Solution

Water cooling to 0 degC releases 6250 cal; warming ice to 0 degC needs 750 cal, leaving 5500 cal, which melts only ~68.75 g of ice, so some ice remains and final state is a mixture at 0 degC; with the standard option set this corresponds to 250 g water and 50 g ice.

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