Specific & Latent Heat

[Cummings]

A couple of anoying problems that i know i should be able to do but are just getting me frustrated.

1. A 50.0-g copper calorimeter contains 250g of water at 20 degrees C. How much steam must be condensed into the water if the final temperature of the system is to reach 50 degrees C

so, the water and the copper colorimeter are gaining heat and the steam is loosing heat via the latent heat of vaporisation.

so
.05 * 387 * (50-20) + .250 * 4180 * (50-20) = 2.26*10^6 * massofsteamrequired

580.5 + 31350 = 2.26*10^6 * massofsteamrequired
so mass of steam required = 14.12g

yet i am told it is meant to be 12.9g

2. In an insulated vessel, 250g of ice at 0 degrees C is added to 600 g of water at 18 degrees C
a, what is the final temperature of the system.
b, how much ice remains when the system reached equilibrium.

for a, the ice is at 0 degrees so it will gain energy from the water for the latent heat of fusion then gain energy as water to reach an equilibrium. the water will loose energy to reach an quilibrium.

i am stuck on this one. I am told the answer is 0 degrees C but i cant find how to get it.

[AKG]

For the second one, figure out how much heat is lost by that much water cooling down that much. Also, figure out how much heat is required to melt the ice. You will find that the heat required to melt the ice is greater than or equal to the heat lost in cooling the water. If they are equal, then the water will come down to zero, and the ice will just have finished melting. If the heat required to melt the ice is greater, then the ice will only be partially finished melting, and in fact the water will start to freeze.

For the first one, realize that the steam is at 100^o\ C, so it will not only have to condense, but cool to 50^o\ C. That process itself will give off heat, so you won't need as much steam.