The thermal efficiencies of combustion engines

The air/fuel ratio can be varied, usually in the range 0.8 (rich) to 1.1 (lean), and a typical limit of the compression ratio is set at about 10 1 by the tendency of the engine to knock at higher ratios, leading to severe mechanical stresses in the engine components. 

The adiabatic expansion and compression serve only to change the temperature of the gas without heat being absorbed or evolved, i.e. iso-entropic changes. The heat changes are therefore only related to the work which is done during the isothermal stages, which is given by 

The modulus indicates that heat is absorbed (+), during the isothermal expansion, but released (—) during the isothermal compression. In the adiabatic processes no heat is supplied or removed from the working gas, and so 

The efficiency, QE, is then defined as the heat absorbed minus the heat released divided by the heat absorbed in the cycle. This expression can, in turn, be transformed to show that the efficiency is equal to the difference between the two temperatures of operation, divided by the upper temperature. 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at thermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by the piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

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