Specific Heat Capacity and Latent Heat

Specific Heat Capacity

We know from the BGE Science course that when materials are heated, the atoms within them vibrate faster (if a solid) or move about with greater Kinetic Energy (if a fluid).

For a fixed amount of heat Energy, the effect varies depending upon the material.

For example, the 100 kJ of heat Energy will:-

Heat 1 kg of Platinum by 769 °C

Heat 1 kg of Copper by 256 °C

Heat 1 kg of Aluminium by 111 °C

Heat 1 kg of Water by 24 °C

Heat 1 kg of Hydrogen Gas by 7 °C

As can be seen, the temperature change varies greatly between materials.

We define Specific Heat Capacity (c) as:-

"The amount of Energy required to raise the temperature of 1 kg of the material by 1°C."

The Specific Heat Capacity can be found using :-

Where :-

Eh = Heat Energy (J)

m = Mass (kg)

C = Specific Heat Capacity (J kg -1 °C -1)

ΔT = Change in Temperature (°C)

Example 1 :-

The Specific Heat Capacity of a material is 2430 J/kg°C. What Energy is required to heat up a 40kg block from 15°C to 60°C?

Eh = ?

c = 2430 J/kg°C

m = 40 kg

ΔT = 60 - 15 = 45 °C

Eh = c m ΔT

= 2430 x 40 x 45

= 4374000 J

= 4.4 MJ

Note - Specific Heat Capacity only applies to either a Solid, Liquid or a Gas being heated or cooled. If a change of state is involved, we must take into account Latent Heat.

Latent Heat

As stated above, Specific Heat Capacity does not explain the absorption of heat energy during a change of state. This is because changing state is a completely different physical process. The graph below shows how the Temperature of a substance changes when heat is applied:-

In the above graph, the Temperature rises steadily, until a state change is reached. Whilst melting or boiling, even though heat Energy is being added, there is no Temperature change. This 'hidden' energy is referred to as Latent Heat.

Heating a state of Matter - Heat Energy used to raise the temperature by increasing the average Kinetic Energy of the molecules. (Specific Heat Capacity calculations)

Changing State of Matter - Heat Energy used to break molecular bonds, allowing a state change. (Latent Heat calculations).

The amount of Energy required to break these bonds (the Latent Heat) varies between Elements, as well as being dependent upon which change of state is occurring:-

Latent Heat of Fusion - The amount of Energy required to melt 1kg of a solid into a liquid.

Latent Heat of Vaporisation - The amount of Energy required to boil 1kg of a liquid into a gas.

Note - Obviously, to reverse the processes above (eg to freeze a liquid or condense a gas), this is the amount of Heat Energy that must be removed from the material.

The below formula can be used to calculate the amount of energy required to change the state of 1 kg of a substance :-

Eh = mL

Where :-

Eh = Heat Energy Supplied (J)

m = Mass (kg)

L = Latent Heat (Jkg-1)

Example 2 -

If the Latent Heat value of Fusion for water is 330 x103 J kg-1 , Calculate how much ice can be melted into water by supplying 990 kJ?

Eh = mL

m = Eh / L

m = 990x103 / 330x103

m = 3 kg