Specific Heat Capacity and Practical Investigation

What specific heat capacity tells us

Different materials respond differently when energy is transferred to them. The specific heat capacity, $c$, of a substance is the energy required to raise the temperature of 1 kg of that substance by 1 °C, without changing its state. Its unit is joules per kilogram per degree Celsius, written $\text{J/kg °C}$.

A high specific heat capacity means that a large amount of energy is needed for each kilogram to rise by one degree. A low specific heat capacity means that the same energy produces a larger temperature rise. This is a property of the material, not simply a statement about how hot an object is.

For a temperature change with no change of state, the quantities are connected by

$$\Delta E=mc\Delta T$$

where $\Delta E$ is the change in internal energy in joules, $m$ is the mass in kilograms, $c$ is the specific heat capacity in $\text{J/kg °C}$ and $\Delta T$ is the temperature change in °C. Therefore, an experimental value can be found from

$$c=\frac{\Delta E}{m\Delta T}.$$

Notice that $\Delta T$ is a difference: $T_{\text{final}}-T_{\text{initial}}$. A temperature interval of 1 °C has the same size as an interval of 1 K.

Measuring the specific heat capacity of a metal

The aim is to measure the energy transferred to a known mass and the resulting temperature change.

1. Measure the mass of the metal block using a balance and record it in kilograms.
2. Insert an electrical heater and a thermometer or temperature probe into the appropriate holes in the block.
3. Wrap the block in insulation to reduce energy transfer to the surroundings.
4. Connect the heater to a low-voltage power supply through a joulemeter. Record the block's initial temperature.
5. Switch on the heater. Record the energy supplied by the joulemeter and the final temperature after a suitable heating period.
6. Calculate $\Delta T$ and then use $c=\Delta E/(m\Delta T)$.

The heater transfers energy electrically. Most of the useful transfer raises the internal energy and temperature of the block. The joulemeter measures the electrical energy supplied, while the temperature probe measures the block's response.

Take temperature and energy readings at several points rather than relying on only one final reading. Repeating the procedure and calculating a mean helps identify anomalous results. A graph of energy supplied against temperature change should be approximately a straight line; its gradient is $mc$, so dividing the gradient by the mass gives $c$.

Comparing different materials

Repeat the investigation using blocks made from different metals, applying the same measurement method and similar insulation. Calculate $c$ separately for each material: comparing temperature rises alone would be misleading if the masses or supplied energies differed.

Water can also be investigated using an electrical heater and joulemeter. Place a measured mass of water in an insulated container, measure its initial temperature, supply a measured amount of energy and record its final temperature. Stir gently so that the temperature is more uniform, and use a lid where appropriate to reduce energy loss. Keep electrical connections dry.

A material with the larger calculated $c$ requires more energy per kilogram for the same temperature rise. Conversely, if equal masses receive equal amounts of energy, the material with the lower $c$ shows the greater temperature rise.

Uncertainty and improving the investigation

The main limitation is that not all the electrical energy recorded by the joulemeter increases the internal energy of the material. Some warms the heater, temperature probe and container, while some is transferred to the surroundings. If the full joulemeter reading is used as though it all heated the sample, the calculated value of $c$ is generally too high.

Insulation and a lid reduce unwanted transfers. Good thermal contact between the probe and the material improves the temperature measurement, while allowing energy to spread through the sample reduces the effect of hot regions close to the heater. With a liquid, stirring helps achieve a representative temperature.

Hot blocks, heaters and liquids can cause burns, so switch off the supply before handling the apparatus and allow it to cool. When heating water, keep the power supply and electrical connections away from spills.