A temperature sensor is to be placed above a CH₄⁻ air jet flame along the extension of the flame's centerline. It is desired to locate the sensor as close as possible to the flame; however, the maximum-temperature operating limit of the sensor is 1200 K. The system operates at 1 atm and the air and fuel enter at 300 K.

Using the simplified state relationships for a diffusion flame, determine the mixture fraction that would correspond to a sensor temperature limit of 1200 K. Assume a constant specific heat cp of 1087 J/kg-K.