Combustion thermodynamics:\nThe maximum adiabatic flame temperature attainable when a fuel burns in air is __________ the maximum adiabatic flame temperature when the same fuel burns in pure oxygen at the same initial conditions.

Introduction / Context:
Adiabatic flame temperature is the theoretical maximum temperature a reacting mixture can reach when combustion proceeds adiabatically (no heat loss to surroundings) and at specified initial conditions. It is a key design parameter for furnaces, burners, gas turbines, and safety analysis in chemical engineering.

Given Data / Assumptions:

• Same fuel, same initial temperature and pressure in both cases.
• Complete combustion assumed.
• Adiabatic conditions (no heat loss), negligible kinetic and potential energy changes.
• Comparison between two oxidizers: air (contains ~21% O2 and ~79% N2 by volume) versus pure oxygen (100% O2).

Concept / Approach:
The adiabatic flame temperature is found from an energy balance: chemical heat release (lower or higher heating value depending on water phase) is converted into sensible heating of the combustion products. When air is used, a large quantity of inert nitrogen is present. This nitrogen is heated along with the products, absorbing a significant portion of the released energy and thereby lowering the peak temperature. With pure oxygen, there is no nitrogen ballast; fewer total moles are heated, resulting in a higher adiabatic flame temperature.

Step-by-Step Solution:
Write energy balance: heat of reaction = sum of sensible heats of products.Case 1 (air): products include CO2, H2O, and substantial N2 that must be heated.Case 2 (O2): products are mainly CO2 and H2O; no nitrogen ballast to heat.For the same heat release, adding inert N2 increases heat capacity of the mixture, therefore the final adiabatic temperature is lower with air.

Verification / Alternative check:
Look up tabulated adiabatic flame temperatures: for common fuels (methane, hydrogen, CO), values in pure oxygen exceed values in air by several hundred kelvin, confirming the reasoning.

Why Other Options Are Wrong:
Higher than: contradicts the inert-dilution effect of nitrogen in air.Same as: would imply no effect of nitrogen ballast, which is false.Not related to: adiabatic flame temperature is directly related to oxidizer composition.

Common Pitfalls:
Confusing real flames (with heat losses, dissociation) with ideal adiabatic values; forgetting dissociation at very high temperatures can also lower the temperature but does not reverse the comparison trend.

Final Answer:
lower than