Question Bank • QB_FP_147 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: I.C. engine cycles

Question Statement:

An air-standard Diesel cycle has a compression ratio $r = 16$ and a cut-off ratio $r_c = 2.0$. For air, $\gamma = 1.4$. Calculate the thermal efficiency of the cycle as a percentage (round off to 1 decimal place).

Answer Key:

61.4

Step-by-Step Solution & Explanation

Diesel cycle thermal efficiency formula: $\eta_{\text{Diesel}} = 1 - \frac{1}{r^{\gamma - 1}} \left[ \frac{r_c^\gamma - 1}{\gamma(r_c - 1)} \right]$ Here $r = 16$, $r_c = 2.0$, $\gamma = 1.4$. $r^{\gamma - 1} = 16^{0.4} = (2^4)^{0.4} = 2^{1.6} \approx 3.0314$ $\frac{r_c^\gamma - 1}{\gamma(r_c - 1)} = \frac{2.0^{1.4} - 1}{1.4(2.0 - 1)} = \frac{2.639 - 1}{1.4 \times 1} = \frac{1.639}{1.4} \approx 1.1707$ $\eta = 1 - \frac{1.1707}{3.0314} = 1 - 0.3862 = 0.6138 \implies 61.38\% \approx 61.4\%$ Acceptable range: $61.0 - 62.0\%$.
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