The supersonic expansion of an underexpanding argon plasma from a high density arc source with small dimensions into a low-pressure vessel with large dimensions is studied by an extended one-dimensional nonlocal thermal equilibrium fluid model, called SPIRIT. In an expanding plasma the velocity increases and the pressure, the density, and the temperatures decrease severely. In this article the virtual source model is discussed first, which is a model describing the expanding plasma as originating from a virtual source. The virtual source model includes some viscosity and heat transport in simplified form, but most of the viscosity and heat transport contributions are neglected. The SPIRIT code includes the full energy and momentum balances. The inclusion of viscosity and heat sources may lead to deviations from an adiabatic and/or isentropic expansion. The SPIRIT code can analyze the deviations. When deviations are small, the isentropic expressions from gas dynamics can be used to model expanding plasma too. Model outcomes are compared with experimental data.