Question Bank • QB_FP_091 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 of $16$ and a cut-off ratio of $2.0$. Taking the adiabatic index $\gamma = 1.4$, calculate the air-standard thermal efficiency of the cycle in percentage.

Answer Key:

61.38

Step-by-Step Solution & Explanation

Air-standard efficiency of Diesel cycle: $\eta_{\text{th}} = 1 - \frac{1}{r^{\gamma - 1}} \left[ \frac{r_c^\gamma - 1}{\gamma(r_c - 1)} \right]$ Where: - Compression ratio $r = 16$ - Cut-off ratio $r_c = 2.0$ - $\gamma = 1.4$ Calculating terms: $r^{\gamma - 1} = 16^{0.4} = 3.0314$ $r_c^\gamma = 2^{1.4} = 2.6390$ $\frac{r_c^\gamma - 1}{\gamma(r_c - 1)} = \frac{2.6390 - 1}{1.4(2 - 1)} = \frac{1.6390}{1.4} = 1.1707$ $\eta_{\text{th}} = 1 - \frac{1}{3.0314} \times 1.1707 = 1 - 0.3862 = 0.6138 = 61.38\%$
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