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 - General Problems - Page 410: 58

Answer

(a) The oven puts energy into the water at a rate of 797 J/s (b) 5.3 grams of water will boil away.

Work Step by Step

The energy $Q$ required to raise the temperature of a substance is: $Q = mc~\Delta T$ We can find the heat energy gained by the water. $Q = m_w~c_w~\Delta T$ $Q = (0.250~kg)(4186~J/kg~C^{\circ})(100~^{\circ}C-20~^{\circ}C)$ $Q = 83,720~J$ We can find the rate at which the oven puts energy into the water. $\frac{Q}{t} = \frac{83,720~J}{105~s}$ $\frac{Q}{t} = 797~J/s$ The oven puts energy into the water at a rate of 797 J/s. (b) We can find the additional energy provided to the water if the oven runs for an additional 15 seconds. $Q = (797~J/s)(15~s) = 11,955~J$ We can find the mass of water which boils away. $Q = m~L$ $m = \frac{Q}{L}$ $m = \frac{11,955~J}{2.26\times 10^6~J/kg}$ $m = 0.0053~kg = 5.3~g$ 5.3 grams of water will boil away.
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