Question

A 9.0×10⁻²-kg ice cube at 0.0 ∘C is dropped into a Styrofoam cup holding 0.35 kg of water at 13 ∘C.

Part A: Find the final temperature of the system. Assume the cup and the surroundings can be ignored.   

Part B: Find the amount of ice (if any) remaining.

Part C: Find the initial temperature of the water that would be enough to just barely melt all of the ice.

Answer 1

A)

as we can notice, we have excess of oxygen that water will reach 0 ^oC before all the ice melts

so,

final temperature of water = 0 ^oC

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B)

To find the amount of ice left

we know, heat lost by water

Q = mcT

Q = 0.35 * 1000 * 13

Q = 4550 cal

this much heat will melt ice of amount

m = 4550 / 80

m = 56.875 grams = 56.875e-2 kg

so,

amount of ice left = 9.0e-2 - 56.875e-2

ice left = 33.125 grams

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C)

to melt 90 grams of ice

Q = 90 * 80 = 7200 cal

if T is the temperature

then

330 * T = 7200

so,

T = 21.818 ^oC