11.3 Phase Change and Latent Heat

Phase Change and Latent Heat

When you add heat to a substance, its temperature doesn't always go up. During a phase change, all the energy goes into breaking or forming bonds between molecules rather than making them move faster. This is called latent heat, and understanding it is essential for analyzing how matter transitions between solid, liquid, and gas states.

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Energy Calculations for Phase Changes

Latent heat is the energy required to change a substance's phase without changing its temperature. There are two types:

• Latent heat of fusion ($L_f$): energy needed to convert between solid and liquid (melting or freezing)
• Latent heat of vaporization ($L_v$): energy needed to convert between liquid and gas (boiling or condensation)

Notice that $L_v$ is always much larger than $L_f$ for the same substance. That's because fully separating molecules into a gas requires far more energy than just loosening them from a solid into a liquid.

The formula for calculating the energy involved in a phase change is:

$Q = mL$

• $Q$ = energy transferred (J)
• $m$ = mass of the substance (kg)
• $L$ = specific latent heat for that transition (J/kg)

Example 1: How much energy is needed to melt 2 kg of ice at 0°C?

Using $L_f = 334{,}000$ J/kg for water:

$Q = 2 \text{ kg} \times 334{,}000 \text{ J/kg} = 668{,}000 \text{ J} = 668 \text{ kJ}$

Example 2: How much energy is needed to vaporize 0.5 kg of water at 100°C?

Using $L_v = 2{,}260{,}000$ J/kg for water:

$Q = 0.5 \text{ kg} \times 2{,}260{,}000 \text{ J/kg} = 1{,}130{,}000 \text{ J} = 1{,}130 \text{ kJ}$

Compare those two results: vaporizing just 0.5 kg of water takes nearly twice the energy of melting 2 kg of ice. This is why steam burns are so dangerous and why boiling a pot of water takes so much longer than melting ice cubes.

Temperature and Energy in Transitions

During a phase transition, the temperature stays constant even though energy is being added or removed. This is the part that trips people up on exams. The energy isn't "disappearing." It's going into changing the arrangement of molecules rather than speeding them up.

• Endothermic transitions (energy absorbed): solid → liquid (melting) and liquid → gas (vaporization). Energy is used to overcome attractive forces between particles, allowing them to move more freely.
• Exothermic transitions (energy released): gas → liquid (condensation) and liquid → solid (freezing). Particles slow down enough for intermolecular attractions to pull them into a more ordered structure, releasing energy in the process.

On a heating curve (temperature vs. energy graph), phase changes appear as flat horizontal segments. The temperature rises during single-phase heating, then plateaus during each phase change. The length of each plateau corresponds to the latent heat for that transition.

Analysis of Phase Diagrams

A phase diagram plots pressure (y-axis) vs. temperature (x-axis) and shows which state of matter a substance occupies under different conditions. It has three main regions (solid, liquid, gas) separated by boundary lines.

The boundary lines represent conditions where two phases coexist in equilibrium. Three special features to know:

• Triple point: the unique temperature and pressure where all three phases coexist simultaneously. For water, this occurs at 0.01°C and 611 Pa (about 0.006 atm).
• Critical point: above this temperature and pressure, the liquid and gas phases become indistinguishable, forming a supercritical fluid. No amount of pressure can liquefy a gas above its critical temperature.
• Sublimation line: the boundary between solid and gas. Along this line, a solid converts directly to gas (sublimation) or gas converts directly to solid (deposition) without passing through the liquid phase.

To determine a substance's state at given conditions:

1. Find the point on the diagram corresponding to the given temperature and pressure.
2. If the point falls within a region, the substance exists in that single phase.
3. If the point falls on a boundary line, two phases coexist in equilibrium.

Examples:

• Water at 1 atm and 25°C falls in the liquid region.
• $CO_2$ at 1 atm and -80°C falls in the solid region (this is dry ice). At 1 atm, $CO_2$ sublimes rather than melts because its triple point is above 1 atm (5.1 atm), so liquid $CO_2$ can't exist at normal atmospheric pressure.

Thermodynamic Concepts in Phase Changes

A few related terms you should be comfortable with:

• Specific heat capacity ($c$): the energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K). You use this with $Q = mc\Delta T$ for heating or cooling within a single phase. During a phase change, you switch to $Q = mL$.
• Enthalpy ($H$): a measure of the total heat content of a system at constant pressure. During a phase change, the enthalpy changes by an amount equal to the latent heat.
• Phase equilibrium: the condition where two phases coexist at a specific temperature and pressure, with molecules transitioning between phases at equal rates so there's no net change.

For multi-step problems (like heating ice at -20°C all the way to steam at 120°C), you'll need to combine $Q = mc\Delta T$ and $Q = mL$ for each segment. Add up the energy for each step: heating the solid, melting, heating the liquid, vaporizing, and heating the gas.