Latent Heat
Heat that changes the phase instead of the temperature.
Lesson at a glanceShow the key points
- During melting or boiling the temperature stays constant; Q = mL (25.2). The same heat is released on freezing or condensing.
- Phase changes separate molecules against attraction: internal energy liquid > solid, vapour > liquid.
- If water can't supply enough heat to melt all the ice, the mixture stays at 0°C.
- Fusion: L = (m₁s₁ + m₂s₂)(θ₁ − θ₂)/m₃ − s₂θ₂.
- Vaporization (steam into calorimeter via a steam trap): (m₁s₁ + m₂s₂)(θ₃ − θ₂) = m₃L + m₃s₂(θ₁ − θ₃).
A pot of water on a stove sits at 100°C for many minutes while it boils away, though the flame pours in heat the whole time. Where does that heat go?
Latent heat
Heat can change a body’s phase instead of its temperature. While a solid melts or a liquid boils, the temperature stays fixed. The heat needed is
Why the temperature stays put
In a solid, strong forces hold molecules nearly in place. In a liquid they are weaker: molecules roam inside but can’t leave the surface. In a vapour the forces are almost nil. Melting and boiling pull molecules apart against attraction, which takes energy without speeding them up. So a body’s internal energy is larger as a liquid than as a solid, and larger again as a vapour.
How much heat turns 0.50 kg of ice at −20°C into steam at 100°C? (s_ice 2100, s_water 4200 J kg⁻¹ K⁻¹; L_f 3.36 × 10⁵, L_v 2.25 × 10⁶ J/kg.)
80 g of ice at 0°C is dropped into 300 g of water at 20°C. Take L = 80 cal/g. What happens?
Measuring the latent heat of fusion of ice
Weigh a calorimeter and stirrer (m₁), add water (m₂) at θ₁. Drop in dried pieces of melting ice, stirring, until the temperature falls to its lowest, θ₂ (all ice melted). Weigh again for the ice mass m₃. Heat lost by calorimeter and water = heat to melt the ice and warm it from 0°C to θ₂:
Measuring the latent heat of vaporization of water
Steam from a boiler at θ₁ passes through a steam trap (to remove condensed drops) and bubbles into water at θ₂ in a calorimeter until it warms by about 5°C to θ₃. Weighing gives the mass m₃ of steam condensed. Heat gained by calorimeter and water = heat released by condensing steam plus its cooling from θ₁ to θ₃:
A calorimeter of water equivalent 20 g holds 180 g of water at 20°C. Steam at 100°C is bubbled in until the temperature is 26°C; the mass grows by 2.0 g. Find L (cal/g).
- 1Q = mL for a change of phase at constant temperature; released on freezing or condensing.
- 2Melting and boiling separate molecules against attraction: internal energy rises without a temperature rise.
- 3If the available heat can't melt all the ice, the mixture stays at 0°C.
- 4Fusion: L = (m₁s₁ + m₂s₂)(θ₁ − θ₂)/m₃ − s₂θ₂. Vaporization: (m₁s₁ + m₂s₂)(θ₃ − θ₂) = m₃L + m₃s₂(θ₁ − θ₃).
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