1.7 - Specific Heat Capacity

Different substances have different specific heat capacities

• Heating a substance increases its internal energy - the total energy in the kinetic energy stores and potential energy stores of its particles.
• Temperature measures the average kinetic energy of the particles.
• Different materials need different amounts of energy to change their temperature by the same amount - e.g. 4,200 J to warm 1 kg of water by 1 °C, but only 139 J for 1 kg of mercury.

Specific heat capacity

The specific heat capacity of a substance is the amount of energy needed to raise the temperature of 1 kg of that substance by 1 °C.

• It's also the energy released by 1 kg of a substance for every 1 °C it cools.
• It's a property of the material, so any sample of a given material has the same specific heat capacity.
• Water has a particularly high specific heat capacity (4,200 J/kg°C), making it useful for storing and carrying thermal energy.

The specific heat capacity equation

Where:

• $\mathrm{\Delta }E$ = Change in thermal energy, in joules (J)
• $m$ = Mass, in kilograms (kg)
• $c$ = Specific heat capacity, in joules per kilogram per degree Celsius (J/kg°C)
• $\mathrm{\Delta }\theta$ = Change in temperature, in degrees Celsius (°C)

The symbol $\mathrm{\Delta }$ means 'change in'.

Worked example - Specific heat capacity equation

A 1.5 kg block of aluminium is heated from 22 °C to 62 °C. The specific heat capacity of aluminium is 900 J/kg°C. How much energy is transferred to the block's thermal energy store?