The Moelwyn-Hughes parameter has been utilized to evaluate a number of thermoacoustical parameters, viz., the Beyer nonlinear parameter; the isothermal, isobaric, and isochoric Gruneisen parameters; the repulsive exponent of intermolecular potential; the molecular constant; the fractional available volume; the Sharma thermoacoustical parameter So; and the Anderson-Gruneisen parameter for a wide variety of polymers at different low temperatures. A relationship among the isobaric, isothermal, and isochoric microscopic (lattice) Gruneisen parameters has been examined and analyzed in the case of several polymers. The results have been used to develop understanding of the significance of microscopic factors such as molecular order and intermolecular forces upon macroscopic thermoacoustic properties. The parameter S0 remains invariant with temperature over a wide range and retains, on average, a constant value of 1.10 for several polymers at low temperatures, similar to a wide variety of substances. The present treatment has the distinct advantage that several thermoacoustic parameters can be evaluated from the knowledge of volume expansivity data alone.