Section 7.7: Heat Capacity and Latent Heat

This section integrates the concepts of specific heat capacity and latent heat to calculate the total energy change when a substance is heated and undergoes phase changes.

Heating without phase change: \[ Q = m c \Delta T \]
Phase change: \[ Q = m L \]

Where:
\( Q \) = heat energy (J)
\( m \) = mass (kg)
\( c \) = specific heat capacity (J/kg·K)
\( \Delta T \) = temperature change (K)
\( L \) = latent heat (J/kg)

Example 1: Heating Ice to Steam

Calculate the energy required to heat 0.2 kg of ice at -10 °C to steam at 100 °C. (Specific heats: ice 2.1×10³ J/kg·K, water 4.18×10³ J/kg·K, latent heats: fusion 3.34×10⁵ J/kg, vaporization 2.26×10⁶ J/kg)

1. Heat ice to 0 °C: \( Q_1 = 0.2 \cdot 2100 \cdot 10 = 4200 \, \text{J} \)
2. Melt ice: \( Q_2 = 0.2 \cdot 334{,}000 = 66{,}800 \, \text{J} \)
3. Heat water to 100 °C: \( Q_3 = 0.2 \cdot 4180 \cdot 100 = 83{,}600 \, \text{J} \)
4. Vaporize water: \( Q_4 = 0.2 \cdot 2{,}260{,}000 = 452{,}000 \, \text{J} \)
Total energy: \( Q_\text{total} = 606{,}600 \, \text{J} \)

Practice Problems

  1. Calculate energy needed to heat 0.5 kg of ice from -5 °C to water at 0 °C.
  2. Determine energy to heat 1 kg of water from 20 °C to 100 °C.
  3. Find energy to convert 0.3 kg of water at 100 °C to steam.
  4. Calculate total energy to heat 0.1 kg of ice at -10 °C to water at 50 °C.
  5. Discuss why latent heat dominates energy calculations during phase changes.
  6. A 200 g ice cube at -5 °C is added to 1 kg of water at 25 °C. Find final temperature.
  7. Compare energy required to melt 100 g ice and heat 100 g water by 80 °C.
  8. Compute energy to heat 2 kg of water from 50 °C to 100 °C and vaporize half of it.
  9. A metal sample releases 10,000 J while solidifying. Determine its latent heat.
  10. Explain the role of specific heat and latent heat in calorimetry experiments.
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