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On a winter day tap water is at 20 C and the room is at 5 C. A tank holds 500 cm³ of water for household use. If all the heat released as this water cools to room temperature could instead be used to lift a 10 kg mass vertically, to what height could the mass be raised? (g = 10 m/s², density of water = 1000 kg/m³, specific heat = 4200 J/kg-C.)

1. 255 m
2. 275 m
3. 295 m
4. 315 m

Correct answer: 315 m

Solution

The 0.5 kg of water cooling by 15 C releases Q = 0.5*4200*15 = 31500 J; setting this equal to mgh = 10*10*h gives h = 315 m.

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