We use in situ transmission electron microscopy to monitor in real time the evaporation of gold, copper, and bimetallic copper-gold nanoparticles at high temperature. Besides, we extend the Kelvin equation to two-component systems to predict the evaporation rates of spherical liquid mono- and bimetallic nanoparticles. By linking this macroscopic model to experimental TEM data, we determine the surface energies of pure gold, pure copper, Cu_{50}Au_{50}, and Cu_{25}Au_{75} nanoparticles in the liquid state. Our model suggests that the surface energy varies linearly with the composition in the liquid Cu-Au nanoalloy; i.e., it follows a Vegard's rulelike dependence. To get atomic-scale insights into the thermodynamic properties of Cu-Au alloys on the whole composition range, we perform Monte Carlo simulations employing N-body interatomic potentials. These simulations at a microscopic level confirm the Vegard's rulelike behavior of the surface energy obtained from experiments combined with macroscopic modeling.