14.2.1 Specific Heat Capacity

Specific Heat Capacity Definition

• The specific heat capacity of a substance is defined as:

The amount of thermal energy required to raise the temperature of 1 kg of a substance by 1 °C

• This quantity determines the amount of energy needed to change the temperature of a substance
• The specific heat capacity is measured in units of Joules per kilogram per Kelvin (J kg^-1 K^-1) or Joules per kilogram per Celsius (J kg^-1 °C^-1) and has the symbol c
  • Different substances have different specific heat capacities
  • Specific heat capacity is mainly used in liquids and solids

• From the definition of specific heat capacity, it follows that:
  • The heavier the material, the more thermal energy that will be required to raise its temperature
  • The larger the change in temperature, the higher the thermal energy will be required to achieve this change

Specific Heat Capacity Equation

• The amount of thermal energy Q needed to raise the temperature by Δθ for a mass m with specific heat capacity c is equal to:

ΔQ = mcΔθ

• Where:
  • ΔQ = change in thermal energy (J)
  • m = mass of the substance you are heating up (kg)
  • c = specific heat capacity of the substance (J kg^-1K^-1or J kg^-1 °C^-1)
  • Δθ = change in temperature (K or °C)

Low v high specific heat capacity

• If a substance has a low specific heat capacity, it heats up and cools down quickly
• If a substance has a high specific heat capacity, it heats up and cools down slowly
• The specific heat capacity of different substances determines how useful they would be for a specific purpose eg. choosing the best material for kitchen appliances

Table of values of specific heat capacity for various substances

• Good electrical conductors, such as copper and lead, are also excellent conductors of heat due to their low specific heat capacity

Step 1:            Calculate the Energy from the power and time

Energy = Power × Time

Power = 1.7 kW = 1.7 × 10³ W

Time = 3.5 minutes = 3.5 × 60 = 210 s

Energy = 1.7 × 10³ × 210 = 3.57 × 10⁵ J

Step 2:            Thermal energy equation

ΔQ = mcΔθ

Step 3:            Rearrange for specific heat capacity

Step 4:            Substitute in values

m = 650 g = 650 × 10^-3 kg

Δθ = 100 - 25 = 75^oC