Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 14 - Heat - Problems - Page 408: 13

Answer

It will take 402 seconds to boil the water.

Work Step by Step

We can find the mass of the water as: $m = \rho~V$ $m = (1000~kg/m^3)(0.75~L)(\frac{10^{-3}~m^3}{1~L})$ $m = 0.75~kg$ We can find the energy required to raise the temperature of the water by $89^{\circ}C$; $Q_w = mc~\Delta T$ $Q_w = (0.75~kg)(4186~J/kg~C^{\circ})(89^{\circ}C)$ $Q_w = 279,415.5~J$ We can find the energy required to raise the temperature of the aluminum by $89^{\circ}C$; $Q_a = mc~\Delta T$ $Q_a = (0.280~kg)(900~J/kg~C^{\circ})(89^{\circ}C)$ $Q_a = 22,428~J$ We can find the total amount of energy required as: $Q = Q_w+Q_a$ $Q = 279,415.5~J+22,428~J$ $Q = 301,843.5~J$ We can find the time required for the coffeepot to produce this amount of energy as: $t = \frac{Q}{P}$ $t = \frac{301,843.5~J}{750~W}$ $t = 402~seconds$ It will take 402 seconds to boil the water.
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