Ambient pressure characteristics of heavy-fermion compounds, such as the ratio of the low temperature magnetic susceptibility to the electronic specific heat coefficient γ and a simple relationship between the T2-coefficient of resistivity and γ2, suggest that a single-energy scale T0 dictates the physics of these materials. Such is the case for Kondo-impurity systems to which heavy-fermions are related. We consider the consequences of assuming that the electronic free energy is given by a universal function of T/T0(V) where V is the molar volume. We show that volume-dependent magnetic susceptibility, specific heat and electrical resistivity of some heavy-fermion compounds scale as T/T0(V), at least over a range in pressures and temperatures. A further consequence of the principle assumption is that Gruneisen parameters defined as ∂ln X/∂ln V, where X is some physical property, should be identical for all properties and equal to that determined from electronic contributions to the volume-thermal expansion coefficient and specific heat. In several materials, this equality holds, at least approximately. Although evidence is found for single-energy scaling in heavy-fermion materials, we cannot conclude unambiguously that the basic assumption is correct in detail. © 1994 Plenum Publishing Corporation.