Optimum Compression Ratio for an Otto Cycle Engine

by Andrew Flores

Submitted : Fall 2011

“The Otto cycle is a thermodynamic cycle that mimics a single cylinder of an automobile engine… Determine the compression ratio that will maximize the net work done per cycle and the corresponding work/cycle. Also, determine the temperature and pressure in all four states described above.”

For my project, I was instructed to find the compression ratio that enables the engine to work most effectively, and to find what the work done at the compression ratio. I am given a handful of equations and values of temperature, pressure, and volume that correspond to points on two graphs, and I am told to find the missing values. The graphs show the changes to pressure, volume, and temperature as the piston moves in the engine’s cylinder.

Algebraic manipulation and substitution gave me a function of work containing an unknown compression ratio. Since the maximum value of work has a tangent line with a slope of zero, I simplified the function set its derivative equal to zero. I solved for the optimum compression ratio and found it equal to 17.932:1. The calculated compression ratio replaced its variables in the original work function to show the net work equals .1639 kilojoules. I solved for all the missing temperatures, pressures, and volumes and used them to verify my answer.

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