In this work 885 new experimental densities values are reported for tetraethylene glycol dimethyl ether (TEGDME), heptane, and nine of their mixtures in the compressed liquid phase over the whole composition range, between (278.15 and 353.15) K and for pressures up to 25 MPa or the lowest of either near the appearance of liquid-liquid equilibrium (LLE) of this mixture. The density measurements were performed with an Anton Paar DMA 60/512P vibrating tube densimeter and then correlated by using a Tammann-Tait equation with standard deviations always smaller than or equal to 2 x 10-4 g.cm(-3). For the TEGDME + heptane mixtures an increase of pressure at constant temperature favors the appearance of a second liquid phase. The isothermal compressibility, the isobaric thermal expansivity, the internal pressure, and the excess molar volume have been determined from the density data. The isothermal compressibility and the isobaric thermal expansivity decrease when the pressure increases and rise with the temperature increase. The internal pressure increases with the polyether mole fraction. Over the entire temperature and pressure ranges the excess molar volume is positive and asymmetrical toward low TEGDME composition.