A $10\%$ rich mixture of Heptane $(C_7{H}_{16})$ and air is initially at a pressure of $1$ bar and

temperature of $100C,$ and is polytropically compressed through a volumetric ratio of $6$ to

It is ignited and adiabatic combustion proceeds at constant volume. The maximum

temperature reached is $2627C$ and at this temperature the equilibrium constants are

$\frac{p_{H_{2}O}{P}_{CO}}{P_{C{O}_2}{P}_{H_2}}=6\mathrm{.}72$

$\frac{P_{CO}^2{P}_{O_2}}{P_{CO}^2{p}^0}=0\mathrm{.}054$

$p^0=1$ bar is a reference pressure for the equilibrium constants. if the constituents of the

gas are $C{O}_2,CO,H_{2}O,H_2,O_2$ and $N_2$ :

$($a$)$ Calcuate the reaction equation without dissociation

$($b$)$ Calculate the equilibrium product composition.

$($c$)$ Verify that approximately $30\mathrm{.}2\%$ of the carbon has burned incompletely.

Notes:

the number of moles is not conserved in this reaction!

You may use any method to solve the $($nonlinear$)$ equations you derive.