A 250g piece of ice at 0.0 degrees C is placed in 200g of water at 100 degrees C. What is the final temp.?

Specific heat of ice is unnecessary for this question and (although it probably won't make a difference), I think the currently accepted values for heat of fusion and specific heat of water are 334 J/g and 4.18 J/g degrees C.

The first step is to find the amount of heat absorbed by the ice in order to melt. This is simply number of grams*heat of fusion, which is 83500 joules. Then, use the formula q=mCdeltaT, in which q is heat, m is mass, C is specific heat, and delta T is the change in temperature.

83500=200(4.18)x

83500=836x

99.88=x

I guess I should have used the values you gave, but 99.88 is close enough to 100 that we can reasonably assume that's what the answer would have come out to. Since the change in temperature was 100 degrees C and it decreased, 100 degrees C-100 degrees C=0 degrees C

a) 0.0 degrees

Lets say the ice is going to melt and reach a temperature of X

The the energy required (J) by the ice first melting and then reaching that temperature will be

250 x 335 + 250 x 4.2 (X-0) = 83750 + 1050X

The energy released (J) by the hot water cooling to X will be

200 x (100 - X) x 4.2 = 84000 - 840X

Now these 2 quantities will be equivalent so

83750 + 1050X = 84000 - 840X

and solving gives...

1890X = 250

X=0.13 deg C

so I'd also choose answer a.

at 0 C, water can be either solid or liquid, so no heating needs to occur to melt the ice. The ice will absorb 83750 J in order to melt.

The water has to give the energy, so it would have to drop in temperature. dividing the total energy lost (83750) by the number of grams (200) gives us the amount of energy lost by each gram of water (418.75 J). Divide this amount by the J/g per C degree of water (4.2) and we get the final temperature drop of the water (99.70).

As we can see, the water is very close to 0 degrees (0.3) before the ice has melted, so the final temperature of the water and melted ice will be between 0.0 and 0.3, or effectively 0.0.

The answer is most likely A.