Final answer:
The calculation of emissivity for a gas mixture within a furnace at 1500 K involves applying principles of thermal radiation and thermodynamics. Specific data or relationships that determine individual gas contributions to the total emissivity are needed and are not provided in the question.
Step-by-step explanation:
The question relates to the determination of emissivity of a gaseous mixture within a furnace, specifically in the context of thermal radiation. Emissivity is a measure of how effectively a material emits thermal radiation compared to a perfect black body. Given that the furnace contains 16% CO₂, 10% H₂O, and non-radiating gases at a temperature of 1500 K and a pressure of 1 atm, the solution requires the application of principles from thermodynamics and heat transfer, potentially encompassing the use of the Stefan-Boltzmann law and the concept of partial pressures of gases contributing to the total emissivity of the mixture.
Unfortunately, the question requires specific data or relationships that determine the contribution of each gas to the total emissivity, which are not provided. This is a complex calculation that depends on the properties of gases involved and possibly their interaction at the stated conditions.