  The low Mach number limit for one-dimensional non-isentropic compressible
Navier-Stokes system without viscosity is investigated, where the density and
temperature have different asymptotic states at far fields. It is proved that
the solution of the system converges to a nonlinear diffusion wave globally in
time as Mach number goes to zero. It is remarked that the velocity of diffusion
wave is proportional with the variation of temperature. Furthermore, it is
shown that the solution of compressible Navier-Stokes system also has the same
phenomenon when Mach number is suitably small.
