Different materials need DIFFERENT amounts of energy to raise their temperature by the same amount. This is described by SPECIFIC HEAT CAPACITY (c).
DEFINITION:
The specific heat capacity of a substance is the amount of energy needed to raise the temperature of 1 kg of the substance by 1°C.
EQUATION:
ΔE = m × c × Δθ
ΔE = change in thermal energy (J)
m = mass (kg)
c = specific heat capacity (J/kg°C)
Δθ = temperature change (°C)
Common SHC values:
Water: 4200 J/kg°C
Aluminium: 900 J/kg°C
Iron/steel: 450 J/kg°C
Copper: 385 J/kg°C
Water has a very HIGH SHC — it takes a lot of energy to heat it. This makes it ideal for carrying and storing thermal energy.
Using the SHC Equation
The equation ΔE = mcΔθ can be rearranged:
Δθ = ΔE ÷ (m × c)
m = ΔE ÷ (c × Δθ)
c = ΔE ÷ (m × Δθ)
EXAMPLE 1 — Energy needed:
Heat 2 kg of water from 20°C to 100°C:
Δθ = 100 − 20 = 80°C
ΔE = 2 × 4200 × 80 = 672,000 J = 672 kJ
EXAMPLE 2 — Temperature change:
27,000 J heats a 3 kg aluminium block (c = 900 J/kg°C):
Δθ = 27,000 ÷ (3 × 900) = 27,000 ÷ 2700 = 10°C
The same equation applies when objects COOL — ΔE is the energy released.
Applications of Specific Heat Capacity
WHY WATER IS USED IN RADIATORS AND COOLING SYSTEMS:
High SHC = carries large amounts of thermal energy per kg per °C → less water needed to heat a room.
Car cooling systems: water absorbs heat from the engine efficiently.
Oceans: high SHC means they absorb huge amounts of solar energy → moderate coastal climates.
REQUIRED PRACTICAL:
RP14 — Determine the SHC of a material:
Heat a known mass with an electric heater of known power.
Record temperature change over time.
Energy input: E = P × t
Compare to ΔE = mcΔθ → rearrange for c.
SOURCES OF ERROR in RP14:
Heat loss to surroundings → measured c higher than true value.
Heat not fully transferred to material → same direction of error.
Minimise by lagging (insulating) the material being heated.
⚠️ Common Mistake
Temperature change (Δθ) is final temperature MINUS initial temperature — not the final temperature alone. If water heats from 20°C to 60°C, Δθ = 40°C, not 60°C. Also: mass must be in kg — convert grams first (÷1000).
📐 Variables
ΔEChange in thermal energy (ΔE) is measured in joules (J)
mMass (m) is measured in kilograms (kg)
cSpecific heat capacity (c) is measured in J/kg°C (J/kg°C)
ΔθTemperature change (Δθ) is measured in degrees Celsius (°C)
📐 Key Equations
ΔE = m × c × Δθ
📌 Key Note
SHC (c): energy to raise 1 kg by 1°C. ΔE = mcΔθ. Water c = 4200 J/kg°C (very high). Δθ = final − initial. Rearrange for any unknown. RP14: electric heater method. High SHC of water → used in heating systems and car cooling.
🎯 Matching Activity — SHC Application Match
Match each substance and application to the correct SHC fact. — drag the symbols on the right to match the component names on the left.
Water (c = 4200 J/kg°C)
Drop here
Aluminium (c = 900 J/kg°C)
Drop here
Δθ = final − initial temp
Drop here
ΔE = mcΔθ
Drop here
Temperature CHANGE — not the final temperature alone
Highest common SHC — used in central heating, car cooling, moderates ocean climate
Higher SHC than iron — heats more slowly for same energy input
Calculates thermal energy change for any heating or cooling process
⚽ FIFA Worked Examples
SHC Calculation
How much energy is needed to heat 0.5 kg of water from 25°C to 85°C? (c = 4200 J/kg°C)
F
ΔE = m × c × Δθ
I
m = 0.5 kg, c = 4200, Δθ = 85 − 25 = 60°C
F
ΔE = 0.5 × 4200 × 60 = 0.5 × 252,000
A
ΔE = 126,000 J (126 kJ)
🧪 Required Practical
🔬 RP14 (Physics) — Determine the specific heat capacity of a material using an electric heater, thermometer and balance. E = Pt gives energy input; rearrange ΔE = mcΔθ to find c.
Know the method, variables, equipment and how to analyse results.
🎯 Test Yourself
Question 1 of 2
1. A 2 kg iron block (c = 450 J/kg°C) cools from 150°C to 30°C. How much energy is released?
2. Why is water used in central heating systems rather than a cheaper liquid?
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