Question

The graph below represents the Otto-cycle, based on which petrol engines are run.

The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8. What is the ideal efficiency of the engine? Use $\gamma$ = 1.40.

• A. $1-{\left(\frac{88}{10}\right)}^{0.4}$
• B. $1-{\left(\frac{88}{10}\right)}^{0.4}$
• C. $1-{\left(\frac{10}{88}\right)}^{0.4}$
• D. $1-{\left(\frac{10}{88}\right)}^{1.4}$

Answer 1

The correct option is C

$1-{\left(\frac{10}{88}\right)}^{0.4}$

The efficiency of an Otto engine is given by the formula

$e=1-\frac{1}{r^{\gamma -1}}r=$ compression ratio

Substituting for known values we get

$e=1-\frac{1}{(\frac{88}{10}{)}^{1.4-1}}$

$=1-\frac{1}{(\frac{88}{10}{)}^{.4}}=1-{\left(\frac{10}{88}\right)}^{0.4}$