Question

Methane is burning with minimum amount of air to form the stable products. The premixed methane-air mixture is filled in a leak-proof spherical vessel at an initial pressure of 1 bar and 298 K. The vessel is well insulated to avoid thermal energy interaction with the surroundings.The combustible mixture is ignited at the centre of the vessel using an electrical spark. The energy added to the mixture for ignition is negligible. During the combustion process, the pressure of the combustion chamber increased due to the energy released by the fuel. Estimate the peak pressure that is achieved inside the vessel at the end of complete combustion without any dissociation of products. Both the reactants and products are in gas phase.

Answer 1

Combustion transforms energy stored in chemical bonds to heat that can be utilized in a variety of ways.

Slow oxidation accompanied by relatively little heat and no light.

•An equation of state provides a relationship among P, T and V (or r) of a substance

•Ideal gas behavior (neglect intermolecular forces and volume of molecules themselves):

–> P=rRT

–> Pv=RT

–> PV=mRT

–> R=R_universal/MW, R_universal=8314 J/kmol K

•Assumption is appropriate for nearly all systems we will consider in MAE 5310 since high temperatures associated with combustion generally result in sufficiently low densities for ideal gas behavior to be a reasonable approximation.

Aside:

•Real gas laws try to predict true behavior of a gas better than ideal gas law by putting in terms to describe attractions and repulsions between molecules. These laws have been determined empirically or based on a conceptual model of molecular interactions or from statistical mechanics

Examples: van der Waals and Redlich-Kwong equations.

ABSOLUTE (STANDARD) ENTHALPY, hi, AND ENTHALPY OF FORMATION, hºf,i

•For chemically reacting systems concept of absolute enthalpy is very valuable

•Absolute enthalpy = enthalpy that takes into account energy associated with chemical bonds (or lack of bonds) + enthalpy associated only with T

–> Absolute enthalpy, h = enthalpy of formation, h_f + sensible enthalpy change, hs

–In symbolic form:

–In words first equation says:

•Absolute enthalpy at T is equal to sum of enthalpy of formation at standard reference state and sensible enthalpy change in going from Tref to T

•To define enthalpy, you need a reference state at which enthalpy is zero (this state is arbitrary as long as it is same for all species).

–Most common is to take standard state as Tref=298.15 K and Pº=1 atm

–Convention is that enthalpies of formation for elements in their naturally occurring state at reference T and P are zero.

•Example, at Tref=25 ºC and Pº=1 atm, oxygen exists as a diatomic molecule, so:

Hence, the peak pressure that is achieved inside the vessel at the end of complete combustion without any dissociation of products.