All too often, points dealing with some aspect or other of the thermodynamics of powerplants are made which are incomplete, ambiguous, erroneous, or a mixture of all three! The purpose of this note is to try to give a limited, but logical, theoretical analysis of one type of propulsion powerplant, namely the by-pass engine with the possibility of heat exchange between the by-pass air stream and the main gas stream before expansion through the propulsion nozzles. This is a problem to which the solution is not obvious, and which would probably present difficulties to the average student. Heat exchangers are perhaps more of hypothetical rather than practical interest at present, but it is important that a correct thermodynamic approach be made in every case. Nothing is less likely to be engineered than a Carnot engine, and the general line of argument should be of wider appeal than the particular example to which it is applied.