Abstract The authors of the main thermoeconomic methodologies developed in the last two decades have recently focused their efforts on the analysis of dissipative devices, i.e. those components whose productive purpose is neither intuitive nor easy to define. Coherent and unanimously accepted cost structures have been identified for dissipative components, while ambiguities still exist as concerns the cost allocation principles to be adopted. Being this aspect evidently cost-influencing, accurate analyses focused on the subjectivity of results are needed. This paper is structured in two parts. In the Part I an in-depth study of some critical issues arising from the thermoeconomic analysis of a 1.5 MW c industrial chiller is presented. The attention is focused on the role of the condenser and the throttling valve (considered as a limit condition for an expander with very low isentropic efficiency); marginal analyses performed on the condensation pressure and the isentropic efficiency of the expander provided elements to assess the rational of the cost allocation principles. Attempting to refugee any cost allocation criterion based on postulates, the concept of Scope is identified as a possible non-arbitrary basis for cost allocation in dissipative devices; consequently, a new topology is defined, abandoning the conventional classification between dissipative and productive units, toward a new distinction between Product Makers and Product Takers functions. The proposed approach is applied to the cost accounting of the examined chiller, revealing inadequate and less explicative than the conventional thermoeconomic approaches due to its “intrinsically differential” nature. In the Part II of this paper the proposed approach will be applied to an Optimization problem, revealing very flexible and insightful.