An engine operates with air on the gasoline cycle as shown in Figure $1$ with isentropic processes $1-2$ and $3-4.$ If the compression ratio is $12,$ the maximum pressure is $10$ MPa $,$ determine

a$)$ the percentage clearance

$[10]$

b$)$ the indicated mean effective pressure,$($MEP$)$ assuming constant specific heats $k=1\mathrm{.}4,c_p=1\mathrm{.}00k\frac{J}{k}gK$

$[10]$

$\frac{V_c+r_c}{V_c}=12$

$1+v_c=12$