B.1.9—Specific heat and latent heat

Temperature change within a phase

Use

$$Q=mc\Delta T$$

where c is the specific heat capacity. For a given mass, a larger c means more energy is required for the same temperature rise.

Energy during a phase change

Use

$$Q=mL$$

where L is the specific latent heat of fusion or vaporization. This energy changes particle interactions while the temperature remains constant.

Choose the equation

• temperature changes, no phase change: $$Q=mc\Delta T$$
• phase changes at constant temperature: $$Q=mL$$

If a process contains both stages, calculate the energy for each stage and add the signed or positive magnitudes consistently.

Worked example from local Question Bank row 22716

A cable receives $30\,\mathrm{W}$ and initially warms at $35\,\mathrm{mK\,s^{-1}}=3.5\times10^{-2}\,\mathrm{K\,s^{-1}}$. For copper, $c=390\,\mathrm{J\,kg^{-1}\,K^{-1}}$. Using $P=mc(\Delta T/\Delta t)$,

$$m=\frac{30}{390(3.5\times10^{-2})}=2.2\,\mathrm{kg}$$

The rate form is valid during the initial interval when losses are negligible.

Common trap

Do not use a temperature difference in $$Q=mL$$, and do not use $$Q=mc\Delta T$$ across a phase-change plateau.