  In this paper, we are concerned with a model of polytropic gas flow, which
consists the mass equation, the momentum equation and a varying entropy
equation. First, a new technique, to set up a relation between the Riemann
invariants of the isentropic system and the entropy variable $s$, coupled with
the maximum principle, is introduced to obtain the a-priori $L^{\infty}$
estimates for the viscosity-flux approximation solutions. Second, the
convergence framework from the compensated compactness theory on the system of
isentropic gas dynamics is applied to prove the pointwise convergence of the
approximation solutions and the global existence of bounded entropy solutions
for the Cauchy problem of the system with bounded initial data. Finally, as a
by-product, we obtain a non-classical bounded generalized solution
$(\rho,u,s),$ of the original non-isentropic polytropic gas flow, which
satisfies the mass equation and the momentum equation, the entropy equation
with an extra nonnegative measure in the sense of distributions.
