  We derive a new class of exact solutions characterized by the
Szekeres-Szafron metrics (of class I), admitting in general no isometries. The
source is a fluid with viscosity but zero heat flux (adiabatic but irreversible
evolution) whose equilibrium state variables satisfy the equations of state of:
(a) ultra-relativistic ideal gas, (b) non-relativistic ideal gas, (c) a mixture
of (a) and (b). Einstein's field equations reduce to a quadrature that is
integrable in terms of elementary functions (cases (a) and (c)) and elliptic
integrals (case (b)). Necessary and sufficient conditions are provided for the
viscous dissipative stress and equilibrium variables to be consistent with the
theoretical framework of Extended Irreversible Thermodynamics and Kinetic
Theory of the Maxwell-Boltzmann and radiative gases. Energy and regularity
conditions are discussed. We prove that a smooth matching can be performed
along a spherical boundary with a FLRW cosmology or with a Vaidya exterior
solution. Possible applications are briefly outlined.
