# Specific heat capacity

## Heating materials

When materials are heated, the gain and start moving faster. The result is that the material gets hotter.

Temperature is a measure of the average kinetic energy of the molecules.

Different materials require different amounts of energy to change temperature. The amount of energy needed depends on:

• the mass of the material
• the substance of the material ()
• the desired temperature change

It takes less energy to raise the temperature of a block of aluminium by 1°C than it does to raise the same amount of water by 1°C. The amount of energy required to change the temperature of a material depends on the specific heat capacity of the material.

## Heat capacity

The specific heat capacity of water is 4,200 Joules per kilogram per degree Celsius (J/kg°C). This means that it takes 4,200 J to raise the temperature of 1 kg of water by 1°C.

Some other examples of specific heat capacities are:

MaterialSpecific heat capacity (J/kg/°C)
Brick840
Copper385
Lead129

Lead will warm up and cool down fastest because it doesn’t take much energy to change its temperature. Brick will take much longer to heat up and cool down. This is why bricks are sometimes used in storage heaters as they stay warm for a long time. Most heaters are filled with oil (1,800 J/kg°C) or water (4,200 J/kg°C) as these emit a lot of energy as they cool down and, therefore, stay warm for a long time.

The specific heat capacity of a material is the energy required to raise one kilogram (kg) of the material by one degree Celsius (°C).

## Calculating thermal energy changes

The amount of stored or released as the temperature of a system changes can be calculated using the equation:

change in thermal energy = mass × specific heat capacity × temperature change

$\Delta E_{t}=m \times c \times \Delta \Theta$

This is when:

• change in thermal energy (ΔEt) is measured in joules (J)
• mass (m) is measured in kilograms (kg)
• specific heat capacity (c) is measured in joules per kilogram per degree Celsius (J/kg°C)
• temperature change (∆θ) is measured in degrees Celsius (°C)

### Example

Sadie is experimenting with a model steam engine. Before the 0.25 kg of water begins to boil it needs to be heated from 20°C up to 100°C. If the specific heat capacity of water is 4,180 J/kg°C, how much thermal energy is needed to get the water up to boiling point?

$E_{t} = m~c~\Delta \theta$

$E_{t} = 0.25 \times 4,180 \times (100 - 20)$

$E_{t} = 0.25 \times 4,180 \times 80$

$E_{t} = 83,600~J$

Question

How much thermal energy does a 2 kg steel block (c = 450 J/kg°C) lose when it cools from 300°C to 20°C?

$E_{t} = m~c~\Delta \theta$

$E_{t} = 2 \times 450 \times (300 - 20)$

$E_{t} = 2 \times 450 \times 280$

$E_{t} = 252,000 J$

Question

How hot does a 3.5 kg brick get if it’s heated from 20°C by 20,000 J (20 kJ)?

$\Delta E = m \times c \times \Delta \theta$

$\Delta E = \frac{\Delta E}{m \times c}$

$\Delta \theta = \frac{20,000}{3.5 \times 840}$

$\Delta \theta = 6.8°C$

$final~temperature = starting~temperature + change~in~temperature$

$final~temperature=20+6.8$

$final~temperature=26.8°C$