The Evaporating Puddle · AI Generator #GEN-C86401A5

Physics · thermodynamics

Problem

After a summer rainstorm, a shallow puddle of water sits on hot asphalt at temperature T=45°CT = 45°\text{C}. The puddle has a surface area of A=0.50  m2A = 0.50\;\text{m}^2 and is only 2.0  mm2.0\;\text{mm} deep. Water molecules escape from the surface when their kinetic energy exceeds the binding energy Eb=0.42  eVE_b = 0.42\;\text{eV} that holds them to the liquid. Using the Maxwell-Boltzmann distribution, find what fraction of water molecules at the surface have sufficient kinetic energy to evaporate. Assume the molecules need only translational kinetic energy in the vertical direction to escape. Given: kB=8.617×10−5  eV/Kk_B = 8.617 \times 10^{-5}\;\text{eV/K}, molar mass of water M=18.0  g/molM = 18.0\;\text{g/mol}, NA=6.022×1023  mol−1N_A = 6.022 \times 10^{23}\;\text{mol}^{-1}

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