In Example 8.2 we wrote the equation of state in terms of Z = f (T,). The

In Example 8.2 we wrote the equation of state in terms of Z = f (T,ρ). The equation of state is also easy to rearrange in the form Z = f (T,P). Rearrange the equation in this form, and apply the formulas from Section 8.6 to resolve the problem using departures at fixed T and P.

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Example 8.2 Real entropy in a combustion engine A properly operating internal combustion engine requires a spark plug. The cycle involves adia- batically compressing the fuel-air mixture and then introducing the spark. Assume that the fuel- air mixture in an engine enters the cylinder at 0.08 MPa and 20°C and is adiabatically and revers- ibly compressed in the closed cylinder until its volume is 1/7 the initial volume. Assuming that no ignition has occurred at this point, determine the final I and P, as well as the work needed to com- press each mole of air-fuel mixture. You may assume that Cig for the mixture is 32 J/mole-K (independent of 7), and that the gas obeys the equation of state. V PV = RT+ aP where a is a constant with value a = 187 cm³/mole. Do not assume that Cy is independent of p. Solve using density integrals.