This paper is Part I of a study concerned with developing a formal framework for modeling air-cooled gas turbine cycles and deals with basic thermodynamic issues. Such cycles involve gas mixtures with varying composition which must be modeled realistically. A possible approach is to define just two components, air and gas, the latter being the products of stoichiometric combustion of the fuel with air. If these components can be represented as ideal gases, the entropy increase due to compositional mixing, although a true exergy loss, can be ignored for the purpose of performance prediction. This provides considerable simplification. Consideration of three idealized simple cycles shows that the introduction of cooling with an associated thermal mixing loss does not necessarily result in a loss of cycle efficiency. This is no longer true when real gas properties and turbomachinery losses are included. The analysis clarifies the role of the cooling losses and shows the importance of assessing performance in the context of the complete cycle. There is a strong case for representing the cooling losses in terms of irreversible entropy production as this provides a formalized framework, clarifies the modeling difficulties, and aids physical interpretation. Results are presented that show the effects on performance of varying cooling flowrates and cooling losses. A comparison between simple and reheat cycles highlights the ro^le of the thermal mixing loss. Detailed modeling of the heat transfer and cooling losses is discussed in Part II of this paper.