# heat and calorometry

specific heat of water is 4.186 J/gC

heat of fusion of ice is 334 J/g

To melt 100g of ice takes 334 J/g x 100g = 33400 J

Heat stored in water at 100 is

4.186 J/gC x 100g x 100C = 41860 J

so there is more than enough heat to melt all the ice and raise it in temperature. The question is what temperature.

the 33400J lost melting the ice lowered the hot water by:

33400J = 4.186 J/gC x 100g x ΔT

ΔT = 33400 / 418.6 = 80C, so the hot water is at 20 deg.

So we now have 100g of water at 20, and 100g of water at 0 mixed, which gives us 200g of water at 10C