In this work we present for the first time a unified model of a low-current short-length arc between copper electrodes. The model employs one-dimensional fluid description of the plasma in argon and copper vapour at atmospheric pressure and the heat transfer in the electrodes made of copper. The solution of the particle and energy conservation of electrons and heavy particles is coupled with the solution of the Poisson equation, from which the self-consistent electric field is obtained. The operation of the non-refractory cathode is based on thermo-field emission. Heat fluxes from the plasma to the electrodes are considered so that a phase change and evaporation from the cathode and a release of copper atoms into the plasma are taken into account. The influence of the copper atoms and ions on the plasma properties is analysed and discussed. The model's predictions are compared with experimental data and a qualitative agreement is obtained besides the restrictions of the one-dimensional fluid model.