Because specific heat capacity and specific latent heat are *intensive properties*, it is important that we have reliable means of measuring their values.

## Determining the specific heat capacity

There are two common ways of finding the SHC of a substance:

- Electrical method
- Method of mixtures

### Electrical method

- Suitable for liquids
- Measure the mass $m$ of the substance
- Measure the initial temperature $T_i$ of the substance
- Immerse a power heater (immersion heater) with voltage rating $V$ and current rating $I$ into the substance
- Heat the substance for an amount of time $t$
- Measure the final temperature $T_f$ of the substance
- The heat energy supplied to the substance will be $$ \begin{equation}\begin{aligned} E_{heat}=VIt\\ \end{aligned}\end{equation} $$
- Use the formula $E_{heat}=mc(T_f-T_i)$ to find the specific heat capacity $c$ of the substance

- The specific heat capacity will thus be: $$ \begin{equation}\begin{aligned} c=\frac{VIt}{m(T_f-T_i)}\\ \end{aligned}\end{equation} $$

### Method of mixtures

Video:

- Suitable for solids especially metals
- Measure the mass $m_s$ of the solid
- Measure the mass $m_w$ of the water in styrofoam cup
- Place the solid in boiling water for a few minutes to allow the initial temperature of the solid to reach $100\degree C$
- Measure the initial temperature $T_{room}$ of the water in the styrofoam cup
- Transfer the solid from the boiling water to the water in the styrofoam cup
- Keep track of the temperature of this mixture until the water and solid reach a final mutual temperature $T_f$
- The heat energy gained by the water will be

- The heat energy gained by the solid will be

- The heat energy lost by the solid will be the negative of the heat energy gained by the water:

- Thus the SHC of the solid will be