Chapter 9, Problem 9.78P

Methane and 30% excess air are to be fed to a combustion reactor. An inexperienced technician mistakes his instructions and charges the gases together in the required proportion into an evacuated closed tank. (The gases were supposed to be fed directly into the reactor.) The contents of the charged tank are at 25°C and 4.00 atm absolute.

Calculate the standard internal energy of combustion of the methane combustion reaction, $\Delta {\hat{U}}_c^{°}\left(kJ/mol\right)$

1. , taking CO₂(g) and H₂O(v) as the presumed products. Then prove that if the constant-pressure heat capacity of an ideal-gas species is independent of temperature, the
specific internal energy of that species at temperature T(°C) relative to the same species at 25°C is given by the expression

   $\hat{U}=\left(C_p-R\right)\left(T-25°C\right)$

where R is the gas constant. Use this formula in the next part of the problem.

1. You wish to calculate the maximum temperature, T_max(°C), and corresponding pressure,
P_maxatm), that the tank would have to withstand if the mixture it contains were to be accidentally ignited. Taking molecular species at 25°C as references and treating all species as ideal gases, prepare an inlet-outlet internal energy table for the closed system combustion process. In deriving expressions for each ${\hat{U}}_i$at the final reactor condition ( Tmax, Pmax ), use the following approximate values for $C_{pi}\left[kJ/\left(mol\cdot °C\right)\right]$: 0.033 for O ₂,0.032 for N ₂,0.052 for CO ₂, and 0.040 for H ₂O(v). Then use an energy balance and the ideal-gas equation of state to perform the required calculations.

1. Why would the actual temperature and pressure attained in a real tank be less than the values calculated in Part (a)? (State several reasons.)
2. Think of ways that the tank contents might be accidentally ignited. The list should suggest why accepted plant safety regulations prohibit the storage of combustible vapor mixtures.