Chapter 4

Specific Heat Capacity

Specific heat capacity is the heat needed to raise the temperature of 1 kg of a substance by 1 °C, and it explains why some materials heat up faster than others.

Definition

The specific heat capacity c of a substance is the amount of heat required to raise the temperature of 1 kg of the substance by 1 °C (or 1 K). Its SI unit is J kg⁻¹ °C⁻¹. Water has a very high specific heat capacity of about 4200 J kg⁻¹ °C⁻¹, which is why it heats up and cools down slowly.

Key formula

Q = mcθ
Q = heat absorbed or released (J); m = mass (kg); c = specific heat capacity (J kg⁻¹ °C⁻¹); θ = change in temperature (°C).
Rearranged: c = Q / (mθ).

What it means physically

  • A material with a high specific heat capacity needs a lot of heat to warm up and releases a lot of heat when it cools.
  • A material with a low specific heat capacity heats up and cools down quickly (e.g. metals).
  • The large value for water is used in car cooling systems and to moderate the climate near the sea.

Everyday applications

Water is used as a coolant because it can absorb large amounts of heat with only a small temperature rise. Sea breezes occur because land (low c) heats up faster than the sea (high c) during the day.

Worked example

How much heat is needed to raise the temperature of 2.0 kg of water from 25 °C to 55 °C? (c = 4200 J kg⁻¹ °C⁻¹)
θ = 55 − 25 = 30 °C.
Q = mcθ = 2.0 × 4200 × 30 = 252 000 J = 252 kJ.

Remember

  • Use the temperature change θ, not the actual reading.
  • Mass must be in kilograms.
  • High c means slow to heat and slow to cool.

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