## 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: 16

#### Answer

The new temperature of the water is $27.6~^{\circ}C$

#### Work Step by Step

We can find the mass of the water as: $m_w = \rho~V$ $m_w = (1000~kg/m^3)(100~mL)(\frac{1~m^3}{10^6~mL})$ $m_w = 0.10~kg$ The heat energy lost by the copper pellets will be equal to the heat energy gained by the water. We can find the equilibrium temperature $T_e$: $m_c~c_c~\Delta T_c = m_w~c_w~\Delta T_w$ $m_c~c_c~(300^{\circ}C-T_e) = m_w~c_w~(T_e-20^{\circ}C)$ $(m_c~c_c+ m_w~c_w)~T_e = m_c~c_c~(300^{\circ}C)+ m_w~c_w~(20^{\circ}C)$ $T_e = \frac{m_c~c_c~(300^{\circ}C)+ m_w~c_w~(20^{\circ}C)}{(m_c~c_c+ m_w~c_w)}$ $T_e = \frac{(0.030~kg)(390~J/kg~C^{\circ})(300^{\circ}C)+ (0.10~kg)(4186~J/kg~C^{\circ})(20^{\circ}C)}{(0.030~kg)(390~J/kg~C^{\circ})+ (0.10~kg)(4186~J/kg~C^{\circ})}$ $T_e = 27.6~^{\circ}C$ The new temperature of the water is $27.6~^{\circ}C$.

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