SPECIFIC HEAT CAPACITY (c) is the amount of energy needed to raise the temperature of 1 kg of a 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 values:
Water: 4200 J/kg°C — very high
Aluminium: 900 J/kg°C
Iron/steel: 450 J/kg°C
Copper: 385 J/kg°C
Air: ~1000 J/kg°C
Higher SHC = more energy needed per kg per °C = heats up and cools down more slowly.
Using the SHC Equation
Rearrangements:
Δθ = ΔE ÷ (m × c)
m = ΔE ÷ (c × Δθ)
c = ΔE ÷ (m × Δθ)
EXAMPLE 1:
Heat 2 kg of water from 20°C to 80°C (c = 4200 J/kg°C):
Δθ = 80 − 20 = 60°C
ΔE = 2 × 4200 × 60 = 504,000 J
EXAMPLE 2:
54,000 J heats a 3 kg aluminium block (c = 900):
Δθ = 54,000 ÷ (3 × 900) = 54,000 ÷ 2700 = 20°C
REQUIRED PRACTICAL (RP14):
Heat a known mass using an electric heater.
E = P × t (energy in from heater).
Measure Δθ with a thermometer.
Rearrange ΔE = mcΔθ to find c.
Insulate to reduce heat loss.
Applications of Specific Heat Capacity
WHY WATER IS USED IN HEATING SYSTEMS:
Water has one of the highest SHC values of any common liquid.
Can carry large amounts of thermal energy per kg per °C — efficient heat transfer.
Used in: central heating radiators, car cooling systems, industrial heat exchangers.
OCEANIC CLIMATE REGULATION:
Oceans have enormous mass of water with high SHC.
Absorb and store huge amounts of solar energy → release slowly.
Coastal areas have milder, more stable temperatures than inland areas.
COOKING:
Cast iron pans (low SHC ≈ 450 J/kg°C): heat up quickly — responsive.
Ceramic dishes (higher SHC): heat up more slowly but retain heat longer.
CONSERVATION OF ENERGY IN MIXING:
m₁c₁Δθ₁ = m₂c₂Δθ₂ (energy lost by hot = energy gained by cold, in an insulated system)
⚠️ Common Mistake
Δθ is FINAL minus INITIAL temperature — not the final temperature alone. Heating from 20°C to 60°C gives Δθ = 40°C, not 60°C. Also convert mass to kg (not grams) before substituting.
📐 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 °C (°C)
📐 Key Equations
ΔE = m × c × Δθ
📌 Key Note
SHC (c): J per kg per °C. ΔE = mcΔθ. Water c = 4200 J/kg°C (highest common). Δθ = final − initial. Rearrange for any unknown. RP14: electric heater method. High SHC of water → radiators, cooling systems, climate moderation.
🎯 Matching Activity — SHC Calculations
Match each scenario to the correct energy or temperature change. — drag the symbols on the right to match the component names on the left.
504,000 J
Drop here
20°C rise
Drop here
High SHC benefit
Drop here
Δθ = final − initial
Drop here
2 kg water, Δθ = 60°C, c = 4200 — ΔE = 2 × 4200 × 60
Water used in central heating — carries more thermal energy per kg per °C
Temperature CHANGE — not the final temperature alone
54,000 J into 3 kg aluminium (c = 900) — Δθ = 54,000 ÷ 2700
⚽ FIFA Worked Examples
SHC Calculation
How much energy heats 0.5 kg of water from 20°C to 100°C? (c = 4200 J/kg°C)
F
ΔE = m × c × Δθ
I
m = 0.5 kg, c = 4200, Δθ = 100 − 20 = 80°C
F
ΔE = 0.5 × 4200 × 80 = 0.5 × 336,000
A
ΔE = 168,000 J (168 kJ)
🧪 Required Practical
🔬 RP14 (Physics) — Determine SHC of a material: electric heater (E = Pt), thermometer, balance. Rearrange ΔE = mcΔθ for c. Insulate to reduce heat loss errors.
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 200°C to 50°C. How much energy is released?
2. Why is water used as the coolant in car engines rather than a cheaper fluid?
⭐ How Well Do You Understand This Topic?
Be honest with yourself — this helps you know what to revise!
Don't get itGetting thereNailed it!
🤖 Ask Mr Badmus AI
Stuck? Just ask! 💬
I'll use FIFA for calculations and flag Higher/Triple content clearly.