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QB_FP_ADV_018
Question Statement:
An air-standard Diesel cycle has a compression ratio of $r = 16$ and a cut-off ratio of $r_c = 2.0$. The working medium is air with ratio of specific heats $\gamma = 1.40$. The air-standard thermal efficiency of this Diesel cycle expressed as a percentage is ________ (round off to 2 decimal places).
Step-by-Step Solution & Explanation
```
Air-Standard Diesel Cycle Efficiency:
eta_Diesel = 1 - (1 / r^(gamma-1)) * [ (r_c^gamma - 1) / (gamma * (r_c - 1)) ]
```
**Step-by-step Calculation:**
1. Given parameters:
$r = 16, \quad r_c = 2.0, \quad \gamma = 1.4$
2. Compression factor:
$r^{\gamma - 1} = 16^{0.4} = (2^4)^{0.4} = 2^{1.6} = 3.03143$
$\frac{1}{r^{\gamma - 1}} = \frac{1}{3.03143} = 0.32988$
3. Cut-off factor bracket:
$r_c^\gamma = 2.0^{1.4} = 2.63902$
$\frac{r_c^\gamma - 1}{\gamma (r_c - 1)} = \frac{2.63902 - 1}{1.4 \times (2.0 - 1)} = \frac{1.63902}{1.4 \times 1.0} = 1.17073$
4. Thermal efficiency:
$\eta_{\text{Diesel}} = 1 - (0.32988 \times 1.17073) = 1 - 0.38620 = 0.61380 = 61.38\%$
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