Section 7.6: Latent Heat of Fusion and Vaporization
Latent heat refers to the energy absorbed or released by a substance during a phase change, without a change in temperature.
Where:
\( Q \) = heat energy absorbed or released (J)
\( m \) = mass of substance (kg)
\( L \) = latent heat (J/kg)
Latent heat of fusion: energy to melt/freeze 1 kg of a substance.
Latent heat of vaporization: energy to boil/condense 1 kg of a substance.
Example 1: Melting Ice
How much energy is required to melt 0.5 kg of ice at 0 °C? (Latent heat of fusion of ice \( L_f = 334,000 \, \text{J/kg} \))
\[ Q = m L_f = 0.5 \cdot 334{,}000 = 167{,}000 \, \text{J} \] Energy required: 167 kJ
Example 2: Boiling Water
How much energy is needed to vaporize 0.2 kg of water at 100 °C? (Latent heat of vaporization \( L_v = 2.26 \times 10^6 \, \text{J/kg} \))
\[ Q = m L_v = 0.2 \cdot 2.26 \times 10^6 = 452{,}000 \, \text{J} \] Energy required: 452 kJ
Practice Problems
- Calculate the energy needed to melt 1 kg of ice at 0 °C.
- Find the energy required to vaporize 0.5 kg of water at 100 °C.
- A 0.25 kg ice cube is melted and then warmed to 20 °C. Compute total energy absorbed. (Use \( c_\text{water} = 4180 \, \text{J/kg·K} \))
- Determine the latent heat of fusion if 0.3 kg of metal melts after absorbing 120,000 J.
- A 2 kg ice cube is added to 1 kg of water at 30 °C. Find final temperature, assuming no heat loss.
- Explain why temperature remains constant during melting or boiling.
- Calculate energy required to convert 0.1 kg of ice at -5 °C to water at 0 °C.
- Compare latent heat of fusion and vaporization for water. Why is \( L_v \) much larger?
- A 500 g sample of metal releases 90,000 J while solidifying. Find its latent heat.
- Discuss practical applications of latent heat in everyday life.