# 18.1.2 Specific Heat Capacity

### Defining Specific Heat Capacity

• The specific heat capacity of 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 oC-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

#### Calculating Specific Heat Capacity

• 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 oC-1)
• Δθ = change in temperature (K or oC)
• 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
• 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 = 75oC #### Exam Tip

The difference in temperature Δθ will be exactly the same whether the temperature is given in Celsius or Kelvin. Therefore, there is no need to convert between the two since the difference in temperature will be the same for both units. ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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