Comparing Carnot, Stirling, Otto, Brayton and Diesel Cycles

Comparing the efficiencies of the Carnot, Stirling, Otto, Brayton and Diesel cycles can be a frustrating experience for the student. The efficiency of Carnot and Stirling cycles depends only on the ratio of the temperature extremes whereas the efficiency of Otto and Brayton cycles depends only on the compression ratio. The efficiency of a Diesel cycle is generally expressed in terms of the temperatures at the four turning points of the cycle or the volumes at these turning points. How does one actually compare the efficiencies of these thermodynamic cycles? To compare the cycles, an expression for the efficiency of the Diesel cycle will be obtained in terms of the compression ratio and the ratio of the temperature extremes of the cycle. It is found that for a fixed temperature ratio that the efficiency increases with compression ratio for the Otto, Brayton and Diesel cycles until their efficiency is the same as that of the corresponding Carnot cycle. This occurs at the point where the heat input to the cycles is zero. For a fixed compression ratio the efficiency increases with temperature ratio for the Carnot and Stirling cycles but decreases for the Diesel cycle. This is an important factor in understanding how a Diesel cycle can be made to be more efficient than an Otto cycle.