Question Bank • QB_FP_ADV_001 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: Thermodynamic principles of I.C. engines

Question Statement:

An air-standard Dual (Sabathé) combustion cycle operates with a compression ratio $r = 16$. The pressure ratio during constant volume heat addition is $r_p = 1.5$ and the cutoff ratio during constant pressure heat addition is $r_c = 1.2$. Taking adiabatic exponent $\gamma = 1.4$, the thermal efficiency of the cycle is ________ $\%$ (round off to two decimal places).

Answer Key:

66.51

Step-by-Step Solution & Explanation

The thermal efficiency $\eta_{\text{dual}}$ of an air-standard dual cycle is given by: $\eta_{\text{dual}} = 1 - \frac{1}{r^{\gamma - 1}} \left[ \frac{r_p r_c^\gamma - 1}{(r_p - 1) + \gamma r_p (r_c - 1)} \right]$ Given: - $r = 16 \implies r^{\gamma - 1} = 16^{0.4} = 3.03143$ - $r_p = 1.5$ - $r_c = 1.2 \implies r_c^{1.4} = 1.2^{1.4} = 1.28925$ Numerator of bracket: $\text{Num} = (1.5)(1.28925) - 1 = 1.93388 - 1 = 0.93388$ Denominator of bracket: $\text{Den} = (1.5 - 1) + 1.4(1.5)(1.2 - 1) = 0.5 + 1.4(1.5)(0.2) = 0.5 + 0.42 = 0.92$ Bracket factor: $F = \frac{0.93388}{0.92} = 1.01509$ Efficiency: $\eta_{\text{dual}} = 1 - \frac{1.01509}{3.03143} = 1 - 0.33486 = 0.66514 \text{ or } 66.51\%$
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