The adiabatic flame temperature is the maximum temperature of the exiting gas after the combustion of fuel. 1 mole of LIQUID \(n\)-octane \(\ce{{ C }_{ 8 }H_{ 18} }\) was burned completely in a furnace with 50% excess AIR. Assume no octane is left after combustion. Note that the nitrogen gas in air is INERT thus does not react during combustion. The liquid fuel and oxygen enter the furnace at \(25^\circ C\). Determine the adiabatic flame temperature of the exiting gas in degrees Celsius. Round your answer to four significant figures.

Notes:

Air composes of 79 mole % nitrogen and 21 mole % oxygen.

The excess air is defined as the excess amount of air with respect to the stoichiometric amount of air needed to completely combust the fuel.

Data:

Latent heat of vaporization of n-octane at 298.15 K: \(41.53 kJ/mol\)

Standard enthalpies of formation:

\({ C }_{ 8 }H_{ 18(l) }=-208.59\quad kJ/mol\\ C{ O }_{ 2(g) }=-393.51\quad kJ/mol\\ { H }_{ 2 }{ O }_{ (g) }=-241.82\quad kJ/mol\)

- Specific heats of product gases (assumed constant):

\({ C }_{ 8 }H_{ 18(g) }=67.87\quad J/(mol\quad K)\\ C{ O }_{ 2(g) }=45.37\quad J/(mol\quad K)\\ { H }_{ 2 }{ O }_{ (g) }=28.85\quad J/(mol\quad K)\\ { O }_{ 2(g) }=30.25\quad J/(mol\quad K)\\ { N }_{ 2(g) }=29.12\quad J/(mol\quad K)\)

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