The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8. a) What is the ideal efficiency of the engine? Use γ=1.40 b) The engine in a Dodge Viper GT2 has a slightly higher compression ratio of 9.6. How much increase in the ideal efficiency results from this increase in the compression ratio?

Question

The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8.  a) What is the ideal efficiency of the engine? Use γ=1.40  b) The engine in a Dodge Viper GT2 has a slightly higher compression ratio of 9.6. How much increase in the ideal efficiency results from this increase in the compression ratio?

avortarF · Accepted Answer

Step 1  a) We want to calculate the ideal efficiency of the engine when the ratio of heat capacity for the gas used is γ=1.40 Ideal efficiency (e) of the Otto-cycle is given by equation 20.6  1) e=1−(1rγ−1)  Now we can plug these values for r and γ into equation (1) to get the ideal efficiency e  e=1−(18.81.40−1)=0.58=58.0%  Step 2  b) The engine in a Dodge Viper GT2 has a slightly higher compression ration r=9.6. We want to calculate the increase in the ideal efficiency e after increasing the compression ratio. So we will use equation (1) again but we will plug the value for r by 9.6  e=1−(19.61.40−1)=0.594=59.4%  The increse in the ideal efficiency will be given by eb−ea  Increase in e=59.4%−58%=1.4%  The ideal efficiency increase as the compression ratio increase.

The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8.

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