$2.$ An ideal cycle reciprocating engine operates with spark ignition system at sea level,$0$ m with $16$ I displacement volume, which is $4$ time greater than the clearance volume. After the heat addition process, temperature rise to $\backslash (\backslash$mathrm$\{$T$\}=2000^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Sketch $\backslash (\backslash$mathrm$\{$P$\}-\backslash$mathrm$\{$V$\}\backslash )$ and calculate:

a$)$ Compression ratio

b$)$ mass of the air in piston

c$)$ T$\text{'}$s$,$ V$\text{'}$s$,$ P$\text{'}$s in all processes

d$)$ Heat addition and heat rejection in kJ

e$)\backslash (\backslash$eta$\_\{\backslash$mathrm$\{$TH$\}\}\backslash )$ in $\backslash (\backslash \%\backslash )$

f$)$ the mean effective pressure, in kPa

$($Refer table : Properties of the atmosphere at high altitude$)$