Question

The Otto cycle having compression ratio 6 and the conditions of air before isentropic compression is 1 bar and ${27}^{\circ }C$ . The expansion process of Otto cycle is expanded further to make the ideal Atkinson cycle. The maximum pressure in both cycle is 20 bar. The difference in their efficiencies
(only magnitude) is _____%. (Take $\gamma$ for air 1.4)

• A. 3.5

Answer 1

The correct option is A 3.5

$\text{Efficiency of Otto cycle}=1-\frac{1}{(r{)}^{\gamma -1}}$ (where, r= compression ratio)

${\eta }_{Otto}=1-\frac{1}{(6{)}^{1.4-1}}=0.5116=51.16\%$

$\text{Expansion ratio, (e)}=\frac{V_4^{\prime }}{V_2}=\frac{V_4^{\prime }}{V_3}={\left(\frac{P_3}{P_4}\right)}^{1/\gamma }={\left(\frac{P_3}{P_4}\right)}^{1/\gamma }$

$={\left(\frac{20}{1}\right)}^{1-1.4}=8.497$

Compression ratio , r = 6

Efficiency of Atkinson cycle is given by

${\eta }_{Atkinson}=1-\gamma \frac{(c-r)}{(c^{\gamma }-r^{\gamma })}=1-1.4\frac{(8.497-6)}{({8.497}^{1.4}-6^{1.4})}$

$=0.5466=54.66\%$

So, Difference in efficiencies $=54.66-51.16=3.5\%$