Latent Heat & Phase Changes Cheat Sheet

Key Facts

• For a temperature change with no phase change, thermal energy is $Q = mc\Delta T$, where $m$ is mass, $c$ is specific heat, and $\Delta T = T_f - T_i$.
• For a phase change at constant temperature, thermal energy is $Q = mL$, where $L$ is the latent heat for that phase change.
• Melting and freezing use latent heat of fusion, so $Q = mL_f$ at the melting or freezing point.
• Vaporization and condensation use latent heat of vaporization, so $Q = mL_v$ at the boiling or condensation point.
• During melting, vaporization, and sublimation, the substance absorbs energy, so $Q > 0$.
• During freezing, condensation, and deposition, the substance releases energy, so $Q < 0$.
• On a heating curve, sloped segments represent $Q = mc\Delta T$ and flat segments represent $Q = mL$.
• In an insulated calorimetry problem, energy is conserved with $Q_{\text{lost}} + Q_{\text{gained}} = 0$.

Vocabulary

Latent heat

Latent heat is the thermal energy absorbed or released during a phase change without a temperature change.

Specific heat

Specific heat is the energy needed to raise the temperature of $1\,\text{kg}$ of a substance by $1\,^{\circ}\text{C}$ or $1\,\text{K}$.

Latent heat of fusion

Latent heat of fusion, $L_f$, is the energy per kilogram needed to melt or freeze a substance at its melting point.

Latent heat of vaporization

Latent heat of vaporization, $L_v$, is the energy per kilogram needed to vaporize or condense a substance at its boiling point.

Heating curve

A heating curve is a graph of temperature versus heat added that shows temperature increases and phase changes.

Thermal equilibrium

Thermal equilibrium occurs when objects in contact reach the same temperature and no net heat flows between them.