A stoichiometric mixture of propane (left(mathrm{C}_{3} mathrm{H}_{8} ight)) and air is burned in a constant volume bomb.

A stoichiometric mixture of propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) and air is burned in a constant volume bomb. The conditions just prior to combustion are 10 bar and \(600 \mathrm{~K}\). Evaluate the composition of the products allowing for dissociation if the peak temperature achieved is \(2900 \mathrm{~K}\) and show that the combustion process is adiabatic (i.e. the heat transfer is small).

The equilibrium constant for the \(\mathrm{CO}_{2}\) reaction at \(2900 \mathrm{~K}\) is \(K_{p_{\mathrm{r}}}=\frac{p_{\mathrm{CO}_{2}}}{p_{\mathrm{Co}} p_{\mathrm{O}_{2}}^{1 / 2}}=4.50\), and it can be assumed that the degree of dissociation for the water reaction is one quarter of that for the carbon dioxide one. Indicate the processes, including a heat transfer process, on the \(U-T\) diagram. The internal energy of propane at \(25^{\circ} \mathrm{C}\) is \(12,380 \mathrm{~kJ} / \mathrm{kmol}\), and the internal energies of formation for the various compounds are \[\mathrm{CO}_{2}-391032 ; \mathrm{H}_{2} \mathrm{O}-239342 ; \quad \mathrm{CO}-108052 \mathrm{~kJ} / \mathrm{kmol}\]
\([0.0916 ; 0.0229 ; 0.1450 ; 0.0076 ; 0.01527 ; 0.7176]\)