Question

A mixture of 15% ) and 85% O2 (by volume) enters an adiabatic combustion chamber at 500 K. All the O recombines to 02 in the combustion chamber. The process is in steady flow, potential and kinetic energies are small, and no shaft work is done. Show that the temperature of the gas at the exit of the combustion chamber is between 1600 and 1700 K (or has an interpolated value of roughly 1670 K. 1.

Answer 1

Here the mixture of 15% O and 85% O₂   combines to form oxygen molecule.

Let's say only 0.15 kg of O combines with 0.85 O to form O2 molecule.

similarly,

Energy of disassociation of Oxygen molecule is.

O2 + hc/ --> O + O

Reversely energy of formation of oxgen is 22.4 kcal/mol

Let's say one mole of oxygen is produced.

172 kJ/mol of energy is released while producing oxygen molecule.

One Mole of oxygen contains = 32 grams.

Consider the system to be closed the energy is released to increase the temperature.

Energy generated is not converted in potential and kinetic form.

So the energy equation for closed volume is given by

Q= m x C_v x ( T2-T1)

Where = m = 32 x 10^-3  kg

Cv= 0.919 Kj/kg-k

T1 = Initial temperature = 500 k

Q = Enthalpy of formation of oxygen molecule

172 x 10³ = 32 x 10^-3 x 919 x (T2 -500)

T2=1669.75 k