Extra Credit-solutions

# Extra Credit-solutions - kaplan(hmk378 – Extra Credit –...

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Unformatted text preview: kaplan (hmk378) – Extra Credit – Weathers – (17104) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Given: specific heat of water c w = 4180 J / kg · ◦ C A 262 kg cast-iron car engine contains water as a coolant. Suppose the engine’s tempera- ture is 32 ◦ C when it is shut off and the air temperature is 7 ◦ C. The heat given off by the engine and water in it as they cool to air tem- perature is 5 × 10 6 J. (Assume the specific heat of iron is 450 J / kg · ◦ C.) What mass of water is used to cool the engine? Correct answer: 19 . 6411 kg. Explanation: Given : Q lost = 5 × 10 6 J , T h = 32 ◦ C , T l = 7 ◦ C , c e = 450 J / kg · ◦ C , c w = 4180 J / kg · ◦ C , and m e = 262 kg . Q lost = m w c w Δ T w + m e c e Δ T e , where Δ T = Δ T w = Δ T e = T h- T l . Thus m w c w Δ T = Q lost- m e c e Δ T m w = Q lost- m e c e Δ T c w Δ T = Q lost c w Δ T- m e c e c w = 5 × 10 6 J (4180 J / kg · ◦ C)(25 ◦ C)- (262 kg) (450 J / kg · ◦ C) 4180 J / kg · ◦ C = 19 . 6411 kg . 002 10.0 points A 194 kg student eats a 200 Calorie doughnut. To “burn it off”, he decides to climb the steps of a tall building. (1 food Calorie = 10 3 Calories.) The acceleration of gravity is 9 . 8 m / s 2 . How high would he have to climb to expend an equivalent amount of work? Correct answer: 440 . 353 m. Explanation: Given : m = 194 kg , and E = 200 Calorie . At the height of h , he has gained a potential energy of E p = mg h, To “burn it off”, he needs to do that amount of work; i.e. , E p = E = mg h, h = E mg = (200 Calorie)(1000 cal / Cal) (194 kg) (9...
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Extra Credit-solutions - kaplan(hmk378 – Extra Credit –...

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