14.3 Specific heat capacity and specific latent heat
- Syllabus
- 9702–2028–2029
- Topic
- 14.3
- Level
- A2
Learning objectives
Specific heat capacity links energy to mass and temperature change
Specific heat capacity c is the thermal energy required per unit mass to produce unit temperature change in a substance.
Q=mcΔT,c=Q/(mΔT),unitJkg−1K−1
Heating 2.0 kg of water by 5.0 K with c = 4200 J kg⁻¹ K⁻¹ requires Q = (2.0)(4200)(5.0) = 4.2 × 10⁴ J. A change of 5.0 °C is also 5.0 K.
In a perfectly insulated system, energy lost equals energy gained. If 0.54 kg of material P (c=390 J kg⁻¹ K⁻¹) and 0.37 kg of Q (c=910 J kg⁻¹ K⁻¹) both warm by ΔT after receiving 24 kJ, then 24000=[(0.54)(390)+(0.37)(910)]ΔT, giving ΔT=43.8 K.
| Step | Check |
|---|---|
| define system | include substance, container and heater parts only when their heat capacities matter |
| assign each ΔT | final minus initial for that body; use magnitude in an energy-gained/lost ledger |
| conserve energy | total lost + supplied = total gained for the stated insulation model |
Use temperature difference, not absolute temperature. High c means more energy per kilogram per kelvin; it does not guarantee a higher final temperature. Account for losses or apparatus heat capacity unless the problem says they are negligible.
Specific latent heat changes state at constant temperature
Specific latent heat L is the thermal energy required per unit mass to change state at constant temperature.
Q=mL,L=Q/m,unitJkg−1
| Quantity | State change on energy input | Microscopic change |
|---|---|---|
| specific latent heat of fusion L_f | solid → liquid at melting point | particles loosen from fixed arrangement; separation changes modestly |
| specific latent heat of vaporisation L_v | liquid → gas at boiling point | particles separate much more and work is done against intermolecular attraction/ambient pressure |
For a substance, L_v is usually greater than L_f because vaporisation produces a much larger increase in particle separation and intermolecular potential energy and involves more work. During either phase change, average kinetic energy and therefore temperature remain constant.
To melt ice of mass m at 0 °C and then warm the resulting water to θ, total energy gained is Q = mL_f + mc_waterθ. In an insulated ice-water mixture, set this plus any other gains equal to the warm water's mcΔT loss before solving for L_f or final temperature.
Do not use mcΔT during a constant-temperature state change or use mL while temperature changes within one phase. Fusion and vaporisation have different L values, and the newly formed phase may require a separate mcΔT term afterward.