Changes of state: specific heat capacity and latent heat (P1.2)
This topic is a reliable source of calculation questions. Examiners will give you a formula and expect you to substitute and rearrange correctly. The key distinction is between heating a substance (uses SHC) and changing its state (uses SLH).
Changes of state
When substances change state, the temperature remains constant even though energy is still being transferred. This is because the energy is used to break or form intermolecular bonds, not to increase particle kinetic energy.
| Change | Name | Energy change |
|---|---|---|
| Solid → liquid | Melting | Energy absorbed (endothermic) |
| Liquid → gas | Boiling / evaporation | Energy absorbed (endothermic) |
| Liquid → solid | Freezing / solidifying | Energy released (exothermic) |
| Gas → liquid | Condensing | Energy released (exothermic) |
Heating curves
A heating curve plots temperature against time (or energy input) for a substance being heated:
- Sloped sections = temperature rising (solid heating, liquid heating, or gas heating).
- Flat sections = state change occurring at constant temperature (melting or boiling point).
The flat section at the melting point is where LATENT HEAT is being absorbed.
Specific heat capacity (SHC)
Definition: the amount of energy needed to raise the temperature of 1 kg of a substance by 1°C (or 1 K).
Formula:
Q = m × c × ΔT
Where:
- Q = energy transferred (J)
- m = mass (kg)
- c = specific heat capacity (J/kg/°C)
- ΔT = temperature change (°C)
c for water = 4,200 J/kg/°C c for concrete ≈ 880 J/kg/°C c for copper ≈ 390 J/kg/°C
Water has a very high SHC — it takes a lot of energy to heat it and it releases energy slowly when cooling. This makes it excellent for cooling systems (car radiators, central heating) and means coastal climates are milder.
Worked example:
How much energy is needed to heat 2 kg of water from 20°C to 100°C?
- ΔT = 100 − 20 = 80°C
- Q = 2 × 4,200 × 80 = 672,000 J (672 kJ)
Specific latent heat (SLH)
Definition: the amount of energy needed to change the state of 1 kg of a substance at constant temperature.
Formula:
Q = m × L
Where:
- Q = energy transferred (J)
- m = mass (kg)
- L = specific latent heat (J/kg)
Two types:
- Specific latent heat of fusion (Lf) — energy to melt or freeze (solid ↔ liquid).
- Specific latent heat of vaporisation (Lv) — energy to boil or condense (liquid ↔ gas).
Water values:
- Lf (ice → water) = 334,000 J/kg = 334 kJ/kg
- Lv (water → steam) = 2,260,000 J/kg = 2,260 kJ/kg
The latent heat of vaporisation is much larger than fusion — many more intermolecular bonds are broken when a liquid becomes a gas.
Worked example:
How much energy is needed to melt 0.5 kg of ice at 0°C?
- Q = m × Lf = 0.5 × 334,000 = 167,000 J (167 kJ)
Required practical: specific heat capacity
Method:
- Place a metal block (known mass m) in a well-insulated container.
- Heat with an immersion heater (measure voltage V and current I; time t).
- Energy supplied: Q = V × I × t (joules).
- Measure temperature rise ΔT.
- Calculate: c = Q / (m × ΔT).
- Compare to accepted value — difference due to heat loss to surroundings.
Common Gateway-paper mistakes
- Using mass in grams instead of kg in Q = mcΔT (c values are per kg).
- Forgetting that during a change of state, temperature does NOT change.
- Confusing specific heat capacity (temperature change) with specific latent heat (state change).
- Forgetting to calculate ΔT (not just the final temperature).
- Not recognising that L for vaporisation > L for fusion for the same substance.
AI-generated · claude-opus-4-7 · v3-ocr-combined-science