Question

What happens in the efficiency of an Otto cycle having a compression ratio $10$ when the $\gamma$ decrease $1.5$%
Assume, initial value of $\gamma$ for air is $1.4$

• A. Efficiency decreases by $58$%
• B. Efficiency decreases by $3.27$%
• C. Efficiency increases by $3.27$%
• D. Efficiency increases by $58$%

Answer 1

The correct option is B Efficiency decreases by $3.27$%

$\text{Initial efficiency,}{\eta }_i=1-\frac{1}{(\gamma {)}^{\gamma -1}}=1-\frac{1}{(10{)}^{0.4}}=0.60189$

${\eta }_i=60.19\%$

When $\gamma$% decreases by $1.5$% value of new $\gamma$ is:


${\gamma }_n=1.4\times \frac{(100-1.5)}{100}=1.379\%$

New efficienct is

${\eta }_f=1-\frac{1}{(\gamma {)}^{{\gamma }_n-1}}=1-\frac{1}{(10{)}^{0.379}}=0.5822$

${\eta }_f=58.22$%

So, change in efficiency is $=\frac{58.22-60.19}{60.19}=-0.0327=-3.27\%$

Efficiency decreases by $3.27$%