Heat Associated with a Phase Change

The heat required to melt a substance is called the heat of fusion, or since such processes are normally carried out at constant pressure, the enthalpy of fusion, q_fus = ΔH_fus. Similarly, the heat required for vaporization is the heat (enthalpy) of vaporization, q_vap = ΔH_vap. The heat required to convert a solid directly to the gaseous state is the heat (enthalpy) of sublimation, q_sub = ΔH_sub.

Example

How much heat is required to convert 40 g of ice at -10°C to steam at 120°C? The specific heat capacities of ice, liquid water, and steam are, respectively, 2.1, 4.2, and 2.0 J/g K; q_fus(ice) = 6.02 kJ/mol and q_vap(water) = 40.7 kJ/mol.

The process can be divided into five steps: Heating ice from -10 to 0°C:

(1) q = (40 g)(2.1 J/g·K)(10 K) = 0.84 × 10³ J Melting ice at 0°C:

(2) q = (6.02 kJ/mol)(40 g)/(18.02 g/mol) = 90.3 kJ

Heating water from 0 to 100°C:

(3) q = (40 g)(4.2 J/g•K)(100 K) = 16.8 × 10³ J Vaporizing water at 100°C:

(4) q = (40.7 kJ/mol)(40 g)/(18.02 g/mol) = 90.3 kJ Heating steam from 100 to 120°C:

(5) q = (40 g)(2.0 J/g•K)(20 K) = 1.6 × 10³ J Applying Rule 2, the total heat required is the sum of steps 1–5: