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.

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.