  This work presents a procedure to solve the Euler equations by explicitly
updating, in a conservative manner, a generic thermodynamic variable such as
temperature, pressure or entropy instead of the total energy. The presented
procedure is valid for any equation of state and spatial discretization. When
using complex equations of state such as Span-Wagner, choosing the temperature
as the generic thermodynamic variable yields great reductions in the
computational costs associated to thermodynamic evaluations. Results computed
with a state of the art thermodynamic model are presented, and computational
times are analyzed. Particular attention is dedicated to the conservation of
total energy, the propagation speed of shock waves and jump conditions. The
procedure is thoroughly tested using the Span-Wagner equation of state through
the CoolProp thermodynamic library and the Van der Waals equation of state,
both in the ideal and non-ideal compressible fluid-dynamics regimes, by
comparing it to the standard total energy update and analytical solutions where
available.
