A Styrofoam bucket of negligible mass contains 1.75 kg of water and 0.450 kg of ice. More ice, from a refrigerator at -15.0 ∘C, is added to the mixture in the bucket, and when thermal equilibrium has been reached, the total mass of ice in the bucket is 0.884 kg.

Assuming no heat exchange with the surroundings, what mass of ice was added?

1 answer

The ice water mixture at the beginning and end is at 0 deg C

added x kg of ice

warm up x kg of ice from -15 to 0
Hi = heat into ice = Cice * x *15

That heat has to come from water freezing. Say y kg of water freezes
so
Cice * x * 15 = heat of fusion * y

Amount of ice at the end
so
.884 = .450 + y + x

You now have two equations in x and y. Solve for x :)