A gas engine with a volumetric compression ratio of \(10: 1\) is run on a weak mixture of methane \(\left(\mathrm{CH}_{4}\right)\) and air, with \(\phi=0.9\). If the initial temperature and pressure at the commencement of compression are \(60{ }^{\circ} \mathrm{C}\) and 1 bar respectively, calculate the maximum temperature and pressure reached during combustion at constant volume, taking into account dissociation of the carbon dioxide and water vapour, under the following assumptions

(a) that \(10 \%\) of the heat released is lost during the combustion period and

(b) that compression is isentropic.

Assume the ratio of specific heat, \(\kappa\), when the compression stroke is 1.4 , and the heat of reaction at constant volume for methane is \(-8.023 \times 10^{5} \mathrm{~kJ} / \mathrm{kmol} \mathrm{CH}_{4}\) (see Chapter 10, P10.9).

[2737 K; 71.57 bar].