• id: JME-10-N08
• title: Mixing Problems — Heat Exchange
• tags: calorimetry, mixing, conservation

In an isolated system, total heat exchanged is zero: $\sum m_i c_i \Delta T_i = 0$, or equivalently, heat lost by hotter bodies = heat gained by colder bodies. The final equilibrium temperature:

$T_f = \frac{m_1 c_1 T_1 + m_2 c_2 T_2}{m_1 c_1 + m_2 c_2}$

This is the weighted average temperature. For same material ($c_1 = c_2$): $T_f = (m_1 T_1 + m_2 T_2)/(m_1 + m_2)$. Critical step in problems: always check whether any phase change occurs before calculating. If the heat available is insufficient for complete phase change, the system stays at the phase-change temperature.