College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 14 - Problems - Page 535: 39


$180~grams~$ of ice should be added to the tea.

Work Step by Step

We can find the mass of the tea: $m_t = (1000~kg/m^3)(2.00\times 10^{-4}~m^3) = 0.20~kg$ The heat required to make ice increase in temperature , melt, and increase in temperature as water is equal in magnitude to the loss of heat from the tea as it cools: $m_i~c_i~\Delta T_i+m_i~L+m_i~c_w~\Delta T_w = m_t~c_w~\Delta T$ $m_i~(c_i~\Delta T_i+L+c_w~\Delta T_w) = m_t~c_w~\Delta T$ $m_i = \frac{m_t~c_w~\Delta T}{c_i~\Delta T_i+L+c_w~\Delta T_w}$ $m_i = \frac{(0.20~kg)(4186~J/kg~C^{\circ})(85.0~C^{\circ})}{(2100~J/kg~C^{\circ})(10.0~C^{\circ})+(333\times 10^3~J/kg)+(4186~J/kg~C^{\circ})(10.0~C^{\circ})}$ $m_i = 0.18~kg$ $180~grams~$ of ice should be added to the tea.
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