# Specific heat capacity

If energy is transferred to a block of lead by heating, the lead particles gain . When lead is in the solid state, its particles are only vibrating, but they vibrate faster after being heated. Particles are close together in the solid state, so they are likely to hit each other and transfer energy. Energy is transferred through the block quickly, so the temperature of the block goes up quickly.

The change in temperature of a system depends on:

• the amount of transferred to the system
• the mass of the substance
• the nature of the substance itself

The of a substance is a measure of the amount of thermal energy needed to increase the temperature of a given substance.

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

Different substances have different specific heat capacities. For example, the specific heat capacity of water is 4,180 J/kg°C, but the specific heat capacity of lead is only 129 J/kg°C.

## Calculating thermal energy changes

The change in thermal energy due to temperature changes is calculated using this equation:

change in thermal energy = mass × specific heat capacity × change in temperature

This is when:

• change in thermal energy is measured in joules (J)
• mass is measured in kilograms (kg)
• specific heat capacity is measured in joules per kilogram per degrees Celsius (J/kg°C)
• change in temperature is measured in degrees Celsius (°C)
The word 'specific' in 'specific heat capacity' means per unit mass, usually per kilogram.

### Example

The specific heat capacity for copper is 385 J/kg°C. Calculate the thermal energy change when the temperature of 2.00 kg of copper is changed by 10.0°C.

change in thermal energy = mass × specific heat capacity × change in temperature

= 2.00 × 385 × 10.0

= 7,700 J (7.7 kJ)

Question

The specific heat capacity of water is 4,180 J/kg°C. Calculate the thermal energy change when 0.200 kg of water cools from 100°C to 25.0°C.

change in temperature = (100 - 25) = 75.0°C

change in thermal energy = mass × specific heat capacity × change in temperature

= 0.200 × 4,180 × 75.0

= 62,700 J (62.7kJ)

Question

The specific heat capacity of brick is 840 J/kg°C. Calculate the temperature change when 400 kJ of thermal energy is transferred to a 3.50 kg brick.

400 kJ = 400 × 1,000 = 400,000 J

change in thermal energy = mass × specific heat capacity × change in temperature

Rearrange the equation: