Monte Carlo simulations of heterogeneous systems of copper at liquid-vapor equilibrium have been performed at several temperatures from 1400 to 2000 K, using the EAM potential of Zhou et al. [Phys. Rev. B 69, 144113 (2004)]. Surface tension of the corresponding planar interfaces has been evaluated using thermodynamic and mechanical approaches. We have investigated the impact of the potential and the temperature on the surface tension of liquid copper. For the first time, calculation results are in very good agreement with experiments with a maximum deviation of 2% from experiments. Additionally, the Monte Carlo simulations provide a temperature coefficient (the derivative of surface tension in regard with temperature) in excellent agreement with the experimental coefficient. This was one of the main challenges of the present simulations.