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How do I apply conservation of energy to this problem? You pour 180 g hot coffee...

How do I apply conservation of energy to this problem? You pour 180 g hot coffee at 78.7°C and some cold cream at 7.50°C to a 115-g cup that is initially at a temperature of 22.0°C. The cup, coffee, and cream reach an equilibrium temperature of 64.0°C. The material of the cup has a specific heat of 0.2604 kcal/(kg · °C) and the specific heat of both the coffee and cream is 1.00 kcal/(kg · C). If no heat is lost to the surroundings or gained from the surroundings, how much cream did you add?

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Answer #1

Coffee gets colder and the cup and the cream get hotter. This means coffee loses energy and the cream and the cup gain energy, so from energy conservation,

heat energy lost by coffee = heat energy gained by cup + heat energy gained by cream,

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