Allied & ICAR Exam Bank • ALLIED_1101 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: Engine Thermodynamics

Question Statement:

An ideal air-standard Diesel cycle has a compression ratio $r = 16$ and a cut-off ratio $r_c = 2.0$. Taking the specific heat ratio $\gamma = 1.4$, the air-standard thermal efficiency of the cycle (in %) is:

Answer Key:

61.4

Step-by-Step Solution & Explanation

Efficiency of Diesel cycle: $\eta_{th} = 1 - \frac{1}{r^{\gamma-1}} \left[\frac{r_c^\gamma - 1}{\gamma (r_c - 1)}\right] = 1 - \frac{1}{16^{0.4}} \left[\frac{2^{1.4} - 1}{1.4 (2 - 1)}\right]$. $16^{0.4} = 3.0314$. $2^{1.4} \approx 2.639$. Term $= \frac{1.639}{1.4} \approx 1.1707$. $\eta_{th} = 1 - \frac{1.1707}{3.0314} = 1 - 0.3862 = 0.6138$ or $61.38\%$.
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