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 498: 19

Answer

The sphere is made of iron.

Work Step by Step

The heat energy lost by the metal sphere will be equal to the heat energy gained by the mercury. We can find the specific heat $c_s$ of the sphere: $m_s~c_s~\Delta T_s = m_m~c_m~\Delta T_m$ $c_s = \frac{m_m~c_m~\Delta T_m}{m_s~\Delta T_s}$ $c_s = \frac{(4.08~kg)(140~J/kg~C^{\circ})(99.0^{\circ}C-20.0^{\circ}C)}{(0.500~kg)(300^{\circ}C-99.0^{\circ}C)}$ $c_s = 449~J/kg~C^{\circ}$ Since this specific heat is close to the specific heat of iron, we can conclude that the sphere is made of iron.

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