How Do You Calculate Energy Needed for a Phase Change (Q = mL)?

For IB Physics SL and HL, calculate the energy needed for a phase change using $Q=mL$, where $m$ is the mass and $L$ is the appropriate specific latent heat. The temperature remains constant during the phase change.

The Reasoning

Specific latent heat is the energy required to change the phase of $1\text{ kg}$ of a substance without changing its temperature. Rearrange or substitute into:

$$Q=mL$$

Here, $Q$ is thermal energy transferred in joules ($\text{J}$), $m$ is mass in kilograms ($\text{kg}$), and $L$ is specific latent heat in joules per kilogram ($\text{J kg}^{-1}$).

Choose $L$ according to the phase change:

For example, calculate the energy needed to melt $0.50\text{ kg}$ of ice at its melting point if $L_f=3.34\times10^5\text{ J kg}^{-1}$:

$$Q=mL_f=(0.50)(3.34\times10^5)=1.67\times10^5\text{ J}$$

Therefore, $1.67\times10^5\text{ J}$ must be transferred to the ice. Freezing the same mass would transfer the same magnitude of energy to the surroundings.

The sign or wording depends on the chosen system and direction of transfer. Melting and vaporization require energy transferred into the substance, whereas freezing and condensation release energy to the surroundings. Unless a sign convention is specified, IB calculations usually report the magnitude of $Q$.

For a multi-stage process, calculate each stage separately. Use $Q=mc\Delta T$ for temperature changes within one phase and $Q=mL$ for constant-temperature phase changes, then add the results. Keep all values in SI units.

A common misconception is to use $Q=mc\Delta T$ during the phase change. That equation applies when temperature changes within one phase; $Q=mL$ applies when the phase changes at constant temperature. If both occur, calculate each stage separately and add the energies, such as $Q_{\text{total}}=mc\Delta T+mL$.

Exam Technique

For a Calculate question, show the equation, substitution, and numerical answer. Convert grams to kilograms, select the correct $L$, and do not introduce a temperature change into the (mL) calculation.