Specific Heat Capacity — Quick Summary

Mr Toogood's Physics · Thermal physics

AQA 3.6.2.1
Q = mcΔθ
Heat capacity
Q₁ = Q₂
Mixing (no losses)
IVt = mcΔθ + E
Continuous flow
E = ΔKE + ΔPE
Internal energy

Heat, temperature & internal energy

  • Heat flows from a hotter body to a cooler one — never the reverse — until thermal equilibrium (equal temperature, no net flow) is reached.
  • Internal energy = sum of the randomly distributed kinetic and potential energies of all particles in a body.
  • Internal energy increases when a system is heated or has work done on it (and vice versa).

Specific heat capacity

Diagram illustrating specific heat capacity as energy absorbed per degree of temperature rise

SHC: energy needed to raise 1 kg of a substance by 1 °C.

Q = mcΔθ
  • Q = heat supplied (J)   m = mass (kg)
  • c = specific heat capacity (J kg⁻¹ °C⁻¹ or K⁻¹)
Water's high c (4200 J kg⁻¹ °C⁻¹) vs. copper (385) means water heats and cools far more slowly for the same energy transfer — this is why water is used in heating/cooling systems.

Mixing method: assuming no losses, heat lost by the hotter substance equals heat gained by the cooler one — m₁c₁(θ₁−θ_f) = m₂c₂(θ_f−θ₂).

Measuring SHC: simple method

Simple apparatus for measuring specific heat capacity using an immersion heater

Immersion heater warms a known mass; record I, V, t, θᵢ and θ_f.

Record current, p.d., time and temperature change to find Q=IVt=mcΔθ.

Limitation: heat lost to the surroundings, and heat absorbed by the container/insulation itself, both give a systematically too-high value of c.

Measuring SHC: continuous flow method

Continuous flow apparatus for measuring the specific heat capacity of a liquid

Water flows steadily through a heated tube; two flow rates eliminate heat loss.

Taking two measurements at the same Δθ (different flow rates) means the heat lost to surroundings, E, is identical both times and cancels on subtraction:

c = (IVt − I₂V₂t₂) / [Δθ(m − m₂)]
Advantage: eliminates the systematic heat-loss error of the simple method — no need to know the heat capacity of the apparatus.

Exam essentials

Key equations

  • Q=mcΔθ
  • Q₁=Q₂ (mixing, no losses)
  • c=(IVt−I₂V₂t₂)/[Δθ(m−m₂)]

Why continuous flow wins

  • Same Δθ both trials → heat loss E cancels exactly.
  • No correction needed for the container's own heat capacity.

Common slips

  • Δθ is the same size in °C or K — but absolute T (e.g. in gas law questions) must be in K.
  • Check units of c match the values given (per °C or per K).
  • Don't forget the container/insulation also absorbs heat in the simple method, unless told to ignore it.