Question

A diesel engine is working with a compression ratio of 15 and expansion ratio of 10. The air standard efficiency of the cycle is
$\text{(Assume}\gamma \text{for air=1.4})$

• A. 63.05

Answer 1

The correct option is A 63.05

$\text{Compression ratio,}r=\frac{V_1}{V_2}=15$

$\text{Expansion ratio,}{r}_e=\frac{V_e}{V_s}=10$

$\text{Cut-off ratio}{r}_c=\frac{r}{c}=\frac{V_1/V_2}{V_4/V_3}=\frac{V_3}{V_2}=\frac{15}{10}=1.5[V_1=V_4]$

$\text{Air standard efficiency,}\eta =1-\frac{1}{\gamma }\frac{1}{r^{\gamma -1}}\left[\frac{r_c^{\gamma }-1}{r_c-1}\right]=1-\frac{1}{1.4}\times \frac{1}{{15}^{0.4}}\left[\frac{{1.5}^{1.4}-1}{1.5-1}\right]$

$=0.6305=63.05\%$