A sample of liquid gallium (

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Interacting systems, real gases and phase equilibria

Soft Matter at the Thermal Scale, Ch Nucleation and the lifetime of a metastable phase

Problem

A sample of liquid gallium (Tm=303 KT_m = 303\,\mathrm{K}, molar enthalpy of fusion Δh=5.59 kJ mol−1\Delta h = 5.59\,\mathrm{kJ\,mol^{-1}}) is supercooled by ΔT=8 K\Delta T = 8\,\mathrm{K} below its melting point. Using Δμ≈Δh ΔT/Tm\Delta\mu \approx \Delta h\,\Delta T/T_m per molecule, find the driving force for solidification in joules and in units of kBTk_BT, evaluating kBTk_BT at the sample's actual temperature with the Boltzmann constant kB=1.381×10−23 J K−1k_B = 1.381\times10^{-23}\,\mathrm{J\,K^{-1}}.

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