Question Bank • QB_PARAMETRIC_FP_CYC_005 NAT • 2 Marks

Section 3: Farm Power

Thermodynamic Air Cycles: Otto, Diesel & Dual

Subtopic: Air-standard Diesel cycle and cut-off ratio

Question Statement:

An engine operates on the air-standard Diesel cycle shown in the accompanying P-V diagram with a compression ratio of $r = 16$ and a cut-off ratio of $\rho = 2.0$. Taking $\gamma = 1.4$, the air-standard thermal efficiency is ________ $\%$ (round off to two decimal places). (Variation QB_PARAMETRIC_FP_CYC_005)

Answer Key:

61.38

Step-by-Step Solution & Explanation

For an air-standard Diesel cycle: $\eta_{Diesel} = 1 - \frac{1}{\gamma r^{\gamma - 1}} \left[ \frac{\rho^\gamma - 1}{\rho - 1} \right]$ Substituting $r = 16$, $\rho = 2.0$, and $\gamma = 1.4$: $\rho^\gamma = 2.0^{1.4} = 2.6390$ $\frac{\rho^\gamma - 1}{\rho - 1} = \frac{1.6390}{1.0} = 1.6390$ $\gamma r^{\gamma - 1} = 1.4 \times 16^{0.4} = 1.4 \times 3.0314 = 4.2440$ $\eta_{Diesel} = 1 - \frac{1.6390}{4.2440} = 1 - 0.3862 = 0.6138$ In percentage: $61.38\%$.
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