On the Sign Convention in Thermodynamics: An Asset or an Evil?

In thermodynamics the sign convention normally used is energy added to a system in the form of heat is taken as positive and that added in the form of work is taken as negative – HIP to WIN (heat in positive – work in negative). This is a common sign convention although some texts specify that all forms of energy added to a system as heat or work are positive. However, regardless of the sign convention adopted for heat and work interactions, later in the same text the specified convention is abandoned in favor of magnitudes or absolute values. This occurs particularly in relation to cycle analyses in which the absolute value is used for energy transfers. Generally for reversible cycles there is no proof as to why the ratio of energy added/rejected via heat transfer equals the ratio of the absolute temperatures of the thermal reservoirs. To promote sign convention consistency, this paper develops the appropriate relationship between energy transfers and thermal reservoir temperatures for reversible cycles and applies the result to power producing and power consuming engineering devices.