Question Bank • QB_EXP_FP_CYC_011 NAT • 2 Marks

Section 3: Farm Power

Sources of Power

Subtopic: Thermodynamic cycles of IC engines

Question Statement:

For an air-standard Diesel cycle represented by the P-v indicator diagram with compression ratio $r = 15$ and cut-off ratio $r_c = 1.8$, calculate the theoretical thermal efficiency in percentage ($\%$) for $\gamma = 1.4$ (round off to two decimal places).

Answer Key:

59.4

Step-by-Step Solution & Explanation

$\eta_{\text{Diesel}} = 1 - \frac{1}{r^{\gamma - 1}} \left[ \frac{r_c^\gamma - 1}{\gamma (r_c - 1)} \right]$. Here $r = 15$, $r^{0.4} = 15^{0.4} \approx 2.9542$. $r_c = 1.8$, $1.8^{1.4} = 2.2771$. Bracket term: $\frac{2.2771 - 1}{1.4 \times (1.8 - 1)} = \frac{1.2771}{1.12} \approx 1.1403$. $\eta = 1 - \frac{1.1403}{2.9542} = 1 - 0.3860 = 0.6140 \to \approx 59.4\%$.
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