Topic: Thermodynamics
Calculate the ideal air standard thermal efficiency based on Otto cycle for a petrol engine with a cylinder bore of 70 mm and stroke of 100 mm and clearance volume of 42.78 cm³? Consider ratio of specific heats, $\gamma=1.4$, $\pi=\frac{22}{7}$ and $log_{10}2.5\cong0.4$.
- A. 40%
- B. 50%
- C. 30%
- D. 60%
Answer: D. 60%
Explanation: Swept volume $V_s = \frac{\pi}{4} D^2 L = \frac{22}{7 \times 4} \times (7)^2 \times 10 = 385~cm^3$.
Clearance volume $V_c = 42.78~cm^3$.
Compression ratio $r = \frac{V_s + V_c}{V_c} = \frac{385 + 42.78}{42.78} = \frac{427.78}{42.78} \approx 10$.
Efficiency $\eta = 1 - \frac{1}{r^{\gamma-1}} = 1 - \frac{1}{10^{1.4-1}} = 1 - \frac{1}{10^{0.4}}$.
Given $\log_{10} 2.5 \cong 0.4$, so $10^{0.4} \cong 2.5$.
$\eta = 1 - \frac{1}{2.5} = 1 - 0.4 = 0.6 = 60\\%$.