This paper presents a comparative study of the thermal efficiencies of mechanical heat engines by using a graphical approach based on the pressure-volume ("P-V") diagram. Three types of idealized thermodynamic cycles--the Otto, the Diesel and the Brayton--are compared in pairs. Given the same temperature range within which the engines operate, the Brayton cycle is shown to have the highest efficiency. The effect of the compression ratio on the efficiency is also demonstrated. As the use of algebra and calculus is kept at a minimal level, the differences in the thermal efficiencies are illustrated in an intuitive and straightforward manner, making this approach suitable for teaching thermodynamics and related energy issues for a wide audience base. (Contains 4 figures.)