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 409: 30

Answer

(a) It takes 4.43 hours to reach the boiling point. (b) It takes another 28.4 hours to change all the boiling water to steam, for a total time of 32.8 hours.

Work Step by Step

(a) The energy $Q$ required to raise the temperature of a substance is: $Q = mc~\Delta T$ We can find the heat energy required to raise the temperature of the water and the iron boiler. $Q = m_w~c_w~\Delta T + m_i~c_i~\Delta T$ $Q = (730~kg)(4186~J/kg~C^{\circ})(100~^{\circ}C-18~^{\circ}C) + (180~kg)(450~J/kg~C^{\circ})(100~^{\circ}C-18~^{\circ}C) $ $Q = 2.57\times 10^8~J$ We can find the time required to reach the boiling point. $t = \frac{Q}{P}$ $t = \frac{2.57\times 10^8~J}{5.80\times 10^7~J/hr}$ $t =4.43~hr$ It takes 4.43 hours to reach the boiling point. (b) The energy $Q$ required to change the state of a substance is: $Q = m~L$ We can find the heat energy required to change the boiling water to steam. $Q = m_w~L$ $Q = (730~kg)(2.26\times 10^6~J/kg)$ $Q = 1.65\times 10^9~J$ We can find the time required to change the boiling water to steam: $t = \frac{Q}{P}$ $t = \frac{1.65\times 10^9~J}{5.80\times 10^7~J/hr}$ $t =28.4~hr$ It takes another 28.4 hours to change all the boiling water to steam, for a total time of 32.8 hours.
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