Question

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

Ratios, rates, proportions
ANSWERED
asked 2021-09-20
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 \(\displaystyle\gamma={1.40}\)
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?

Expert Answers (1)

2021-09-21
Step 1
a) We want to calculate the ideal efficiency of the engine when the ratio of heat capacity for the gas used is \(\displaystyle\gamma={1.40}\) Ideal efficiency (e) of the Otto-cycle is given by equation 20.6
1) \(\displaystyle{e}={1}-{\left({\frac{{{1}}}{{{r}^{{\gamma-{1}}}}}}\right)}\)
Now we can plug these values for r and \(\displaystyle\gamma\) into equation (1) to get the ideal efficiency e
\(\displaystyle{e}={1}-{\left({\frac{{{1}}}{{{8.8}^{{{1.40}-{1}}}}}}\right)}={0.58}={58.0}\%\)
Step 2
b) The engine in a Dodge Viper GT2 has a slightly higher compression ration \(\displaystyle{r}={9.6}\). 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
\(\displaystyle{e}={1}-{\left({\frac{{{1}}}{{{9.6}^{{{1.40}-{1}}}}}}\right)}={0.594}={59.4}\%\)
The increse in the ideal efficiency will be given by \(\displaystyle{e}_{{{b}}}-{e}_{{{a}}}\)
Increase in \(\displaystyle{e}={59.4}\%-{58}\%={1.4}\%\)
The ideal efficiency increase as the compression ratio increase.
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