14.3 Phase Change and Latent Heat

Phase Change and Latent Heat

Energy Transfer in Phase Changes

When matter shifts between solid, liquid, and gas states, energy is either absorbed or released. The temperature stays the same during the transition because all that energy goes into breaking or forming intermolecular bonds rather than speeding up or slowing down the particles.

• Melting (solid → liquid) and vaporization (liquid → gas) require energy input. The energy breaks intermolecular bonds, allowing particles to move more freely.
• Freezing (liquid → solid) and condensation (gas → liquid) release energy. Bonds form between particles, and that stored energy gets released into the surroundings.

The amount of energy involved depends on two things: the substance itself and how much mass is changing phase. Every substance has its own characteristic latent heat values, one for melting/freezing and another for boiling/condensation. Water, for instance, requires far more energy per kilogram to vaporize than most common liquids.

Latent Heat Calculations

The core formula for phase change energy is:

$Q = mL$

• $Q$ = energy transferred (joules, J)
• $m$ = mass of the substance (kilograms, kg)
• $L$ = latent heat for the specific phase change (J/kg)

There are two types of latent heat you need to know:

Latent heat of fusion ($L_f$) applies to melting and freezing. For example, to melt 2 kg of ice at 0°C:

$Q = 2 \text{ kg} \times 334 \text{ kJ/kg} = 668 \text{ kJ}$

That same 668 kJ would be released if 2 kg of water froze at 0°C. The magnitude is identical; only the direction of energy flow changes.

Latent heat of vaporization ($L_v$) applies to boiling and condensation. To vaporize 1.5 kg of water at 100°C:

$Q = 1.5 \text{ kg} \times 2{,}260 \text{ kJ/kg} = 3{,}390 \text{ kJ}$

Notice how $L_v$ for water (2,260 kJ/kg) is nearly seven times larger than $L_f$ (334 kJ/kg). Converting liquid water to steam takes much more energy than converting ice to liquid water, because vaporization requires completely separating molecules from one another.

Temperature Effects During Phase Changes

If you plot temperature vs. energy added for a substance being heated, you get a heating curve. The key feature: phase changes show up as horizontal (flat) segments where the temperature holds steady even though energy keeps flowing in.

• The length of each flat segment corresponds to how much energy that phase change requires ($Q = mL$).
• Between phase changes, the temperature rises linearly. The slope of these rising sections depends on the specific heat capacity of the substance in that phase. Since solids, liquids, and gases of the same substance generally have different specific heat capacities, the slopes differ.

A cooling curve works the same way in reverse. Flat segments appear where the substance releases energy during freezing or condensation, and the temperature drops linearly between those transitions.

The big takeaway: during a phase change, added energy doesn't raise the temperature. All of it goes toward changing the arrangement of molecules. Only after the phase change is complete does the temperature start changing again.