An air standard Otto cycle operates with a compression ratio of 9 and the ambient temperature is 300 K. If the adiabatic
index of the medium is 1.5, what is the efficiency?

Correct option is B

​$$\textbf{Given Data:} \\[0.5em]\text{Compression ratio } (r):\ 9 \\\text{Ambient temperature } (T_1):\ 300\ \text{K} \\\text{Adiabatic index } (\gamma):\ 1.5\ \text{(ratio of specific heats, } c_p / c_v)\\[1.5em]\textbf{Otto Cycle Efficiency Formula} \\[0.5em]\text{The thermal efficiency of the Otto cycle is given by:} \\\eta = 1 - \frac{1}{r^{\gamma - 1}} \\[0.5em]\text{where:} \\r = \text{Compression ratio} \\\gamma = \text{Adiabatic index}\\[1.5em]\textbf{Substitute Values} \\[0.5em]\eta = 1 - \frac{1}{9^{1.5 - 1}} = 1 - \frac{1}{9^{0.5}} = 1 - \frac{1}{3} = \frac{2}{3} \approx 0.6667$$​​