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It takes 1 calorie of heat to raise 1 gram or water or ice 1° C, but it takes 80 calories to change 1 gram of ice at 0° C to 1 gram of water at 0° C. It's best to divide the problem into three parts, raising the temperature of the ice, melting the ice, and raising the temperature of the water, then combine the three parts at the end. You can just as easily do it in two parts, combining the two parts in which the temperature is raised, but I'll do it the less confusing way this time.

ice @ -20° to ice @ 0°:

30 g * 20° * 1 cal/°/g = 600 cal

ice @ 0° to water @ 0°:

30 g * 80 cal/g = 2400 cal

water @ 0° to water @ 20°:

30 g * 20° * 1 cal/°/g = 600 cal

(600 + 2400 + 600) cal = 3600 cal

(or 3.6 kilocalories)

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Q: How much heat is necessary to change 30 grams of ice at -20 degrees celsius into water at 20 degrees celsius?
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