Abstract: This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations
ρ_t+(ρu)_x=0 (ρu)_t+(ρu²+p(ρ))_x=0 p(ρ)=k²ρ^γ,1 < γ < 3.
when all the function equations are satisfied
<v,η_iq_j-η_jq_i>=<v,η_i><v,q_j>-<v,η_j><v,q_i>.
where supp v is small,v is a Dirac mass under a strong confine ρ ≥ C(T) > 0.