The equations of ideal gas dynamics with an equation of state, which is separated into a sum of functions of density and entropy, admit a 12-dimensional Lie algebra, which is a direct sum of two ideals.
Following results were obtained:
1. The optimal system of subalgebras was obtained for a 12-dimensional Lie algebra.
2. Using the optimal system was obtained by three subgraphs embedded subalgebras: primary, intermediate and final.
3. Using the chain of embedded subalgebras of final subgraph were calculated invariant submodels (IS) {1.8}, {2.10} and partially IS (PISub) {4.6}, {5.10}.
4. Solutions were embedded one into another.
All solutions IS {2.10} were embedded into solutions IS {1.8}.
If the parameter c=1 then partially invariant solutions (PISol) of rank 1 and defect 1 for PISub {4.6} reduced to the solution IS {2.10}.
If parameter с not equal to 1 then the solution PISub {4.6} can not be reduced to the solution IS {1.8}.
5. It was obtained PISol for PISub {5.10}.