We have an ideal Otto cycle with a compression ratio of:

\(\displaystyle{r}={10.5}\)

Air is injected in to the engine at the next pressure and temperature:

\(\displaystyle{p}_{{{1}}}={90}{k}{P}{a}\)

\(\displaystyle{T}_{{{1}}}={40}°{C}\approx{313}{K}\)

The power of the cycle is:

\(\displaystyle{W}={90}{k}{W}\)

We are to determine the coefficient of efficiency and the rate of heat intake.

The specific heat ratio for air we get from table A-2 and it’s value is:

\(\displaystyle{k}={1.1}\)

The coefficient of thermal efficiency for an Otto cycle with constant specific heats is:

\(\displaystyle\eta={1}-{\frac{{{1}}}{{{r}^{{\kappa-{1}}}}}}\)

\(\displaystyle={1}-{r}^{{{1}-\kappa}}\)

\(\displaystyle={1}-{10.5}^{{{1}-{1.4}}}\)

\(\displaystyle\Rightarrow\eta={0.61}\)

The rate of heat input is: \(\displaystyle\eta={\frac{{\dot{{{W}}}}}{{\dot{{{Q}_{{\in}}}}}}}\)

\(\displaystyle\Rightarrow{Q}_{{in}}={\frac{{\dot{{{W}}}}}{{\eta}}}\)

\(\displaystyle={\frac{{{90}{k}{W}}}{{{0.61}}}}\)

\(\displaystyle\Rightarrow{Q}_{{in}}={147.541}{k}{W}\)