Section 2.3: Calorimetry
Calorimetry is the study of measuring heat transfer during physical or chemical processes. A calorimeter is an insulated device that minimizes energy exchange with the surroundings. The heat lost by one body equals the heat gained by another.
- Heat transfer: \( Q = mc\Delta T \)
- Conservation of energy: \( Q_\text{lost} + Q_\text{gained} = 0 \)
- Thermal equilibrium: hot and cold objects exchange heat until temperatures equalize.
Example 1
A 200 g piece of copper at 150 °C is placed into 100 g of water at 20 °C. Find the final temperature. (\(c_\text{Cu} = 390 \, \text{J/kg·°C}\), \(c_\text{water} = 4186 \, \text{J/kg·°C}\))
Heat lost by copper = Heat gained by water:
\((0.200)(390)(T_f - 150) + (0.100)(4186)(T_f - 20) = 0\)
Expanding: \(-78(T_f - 150) + 418.6(T_f - 20) = 0\)
Simplifying: \(340.6T_f + 3320 = 0 \Rightarrow T_f \approx 26.7 °C\)
Final Temperature: ≈ 27 °C
Practice Problem
A 500 g block of aluminum at 100 °C is placed into 300 g of water at 25 °C. Find the equilibrium temperature. (\(c_\text{Al} = 900 \, \text{J/kg·°C}\))