Question Bank • QB_FP_026 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: I.C. engine cycles

Question Statement:

An ideal air-standard Diesel cycle operates with a compression ratio of $r = 16.0$ and a cut-off ratio of $r_c = 2.0$. Taking the adiabatic index $\gamma = 1.40$, the theoretical thermal efficiency of the cycle expressed in percentage is ________ (round off to 1 decimal place).

Answer Key:

61.4

Step-by-Step Solution & Explanation

Thermal efficiency of an air-standard Diesel cycle is given by: $\eta_{\text{Diesel}} = 1 - \frac{1}{r^{\gamma - 1}} \left[ \frac{r_c^\gamma - 1}{\gamma(r_c - 1)} \right]$ 1. $r^{\gamma - 1} = 16^{0.40} \approx 3.0314$ $\frac{1}{r^{\gamma - 1}} = \frac{1}{3.0314} \approx 0.3299$ 2. For $r_c = 2.0$ and $\gamma = 1.40$: $r_c^\gamma = 2^{1.40} \approx 2.6390$ $r_c^\gamma - 1 = 1.6390$ $\gamma (r_c - 1) = 1.40 \times (2.0 - 1.0) = 1.40$ $\left[ \frac{r_c^\gamma - 1}{\gamma(r_c - 1)} \right] = \frac{1.6390}{1.40} \approx 1.1707$ 3. Thermal efficiency: $\eta = 1 - (0.3299 \times 1.1707) = 1 - 0.3862 = 0.6138 = 61.38\% \approx 61.4\%$
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