## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson

# Chapter 17 - Work, Heat, and the First Law of Thermodynamics - Exercises and Problems - Page 497: 17

#### Answer

The initial temperature of the pan was $272^{\circ}C$ which is $522^{\circ}F$

#### Work Step by Step

We can find the mass of the water as: $m_w = \rho~V$ $m_w = (1000~kg/m^3)(10.0~L)(\frac{1~m^3}{10^3~L})$ $m_w = 10.0~kg$ The heat energy lost by the aluminum will be equal to the heat energy gained by the water. We can find the initial temperature of the pan: $m_a~c_a~\Delta T_a = m_w~c_w~\Delta T_w$ $m_a~c_a~(T - 24.0^{\circ}C) = m_w~c_w~\Delta T_w$ $m_a~c_a~T = m_w~c_w~\Delta T_w+m_a~c_a~(24.0^{\circ}C)$ $T = \frac{m_w~c_w~\Delta T_w+m_a~c_a~(24.0^{\circ}C)}{m_a~c_a}$ $T = \frac{(10.0~kg)(4186~J/kg~C^{\circ})(4.0~C^{\circ})+(0.750~kg)(900~J/kg~C^{\circ})(24.0^{\circ}C)}{(0.750~kg)(900~J/kg~C^{\circ})}$ $T = 272~^{\circ}C$ We can convert this temperature to Fahrenheit. $F = \frac{9}{5}C+32$ $F = \frac{9}{5}(272)+32$ $F = 522$ The initial temperature of the pan was $272^{\circ}C$ which is $522^{\circ}F$.

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