06 / CHAPTER 06
Heat capacity and phase change
Calculate storage and latent-energy requirements.
ANCHOR EQUATION
Sensible heating
In symbols: Q = mcΔT
Heat required for a temperature change depends on mass and heat capacity.
Heat capacity measures energy per temperature change
Specific heat stores sensible energy; latent heat stores energy while a phase changes without changing temperature. The distinction matters in water systems because evaporation and boiling can dominate energy budgets.
Separate sensible and latent terms
For a temperature change within one phase, dQ = mc dT, so Q = mcΔT when c is constant. During a phase transition at fixed temperature, Q = mL, where L is latent heat per mass. A multi-stage process sums these contributions in sequence.
Heating 2 kg of water by 15 K requires Q = mcΔT = 2(4180)(15) = 125.4 kJ. Evaporating just 0.10 kg at L_v ≈ 2.26 MJ/kg requires 226 kJ, more than the sensible heating.
Heat capacity varies and phase change is not optional
Near a phase transition, c and L can depend on pressure and composition. Do not use mcΔT through boiling; temperature can remain nearly fixed while energy changes phase fraction.
Work it: Estimate the energy to heat 5 kg of water from 20°C to 80°C, then compare with evaporating 0.25 kg. Which process would dominate a warm open basin?