(Solved): In a mixture of methane \( \left(\mathrm{CH}_{4}\right) \) and air there are three volumes of oxyge ...

In a mixture of methane \( \left(\mathrm{CH}_{4}\right) \) and air there are three volumes of oxygen to one volume of methane. From initial conditions of 1 bar and \( 95^{\circ} \mathrm{C} \) the gas is compressed reversibly and adiabatically through a volume ratio of 5 . Assuming that air contains only oxygen and nitrogen, calculate: (i) the values of \( c_{p}, c_{v}, \tilde{c}_{p}, \tilde{c}_{v}, R \) and \( \gamma \) for the mixture; (ii) the final pressure and temperature of the mixture; (iii) the work input per unit mass of mixture.