1.1.3 Specific Heat Capacity

In this lesson, you will learn what specific heat capacity is, how it affects how substances and materials heat and cool down, and how knowing the specific heat capacity of a material allows us to calculate how much energy the material has gained or lost (or the change in energy) when heated up or cooled down.

Some materials or substances are more difficult to heat up than others. Remember that heating is the transfer of energy from one object’s thermal energy stores to another object’s thermal energy stores. The reason some objects are harder to heat up than others is because some materials need more energy transferred into their thermal energy stores to go up in temperature than others.

For example, the energy needed to increase the temperature of 1 kg of water by 1 °C is 4,200 J, while the energy needed to increase the temperature of 1 kg of mercury by 1 °C is only 140 J.

The energy required to increase the temperature of 1 kg of any substance by 1 °C is called the specific heat capacity. In the water and mercury example, you found out that water has a specific heat capacity of 4,200 J and mercury has a specific heat capacity of 140 J.

The greater the specific heat capacity of a material, the more energy needs to be transferred to the material for it to go up in temperature. Also, the greater the specific heat capacity of a material, the more energy the material will release when it cools down, since it stored more energy when it was being heated up. One way of thinking about it is that materials with with a larger specific heat capacity can store more energy.

A useful thing that knowing the specific heat capacity of a material lets us work out is how much energy the material has gained when heated up or lost when cooled down. We can calculate this amount of energy stored in or released from a system as its temperature changes using Equation 5 shown below.

\(\Delta E=mc\Delta \theta\)

or

The formula for the change in thermal energy as the temperature of a material changes has four components:

1. \(\Delta E\) is the change in thermal energy of the material or substance. This change can either be an increase or a decrease in energy. \(\Delta E\) has units of joules (J).
2. \(m\) is the mass of the material or substance. \(m\) must always have units of kilograms (kg) when used in this formula.
3. \(c\) is the specific heat capacity of the material or substance. \(c\) has units of joules per kilogram per degree Celsius (J/kg °C).
4. \(\Delta \theta\) is the change in temperature of the material or substance. This change can either be an increase or a decrease in temperature. \(\Delta \theta\) has units of degrees Celsius (°C).