In cooling down to liquid at 0 C, the steam will lose
Q = 540 cal/g*15g + 1.0cal/gC*100C*15g
= 8100 + 1500 = 9600 calories.
That amount of heat, transferred to the ice, can melt
9600 cal/80 cal/g = 120 g of ice.
The 540 cal/g and 80 cal/g numbers that I used are the heats of vaporization and fusion, respectively.
Find the mass of 0 degree C ice that 15 g of 100 degree Csteam will completely melt.
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