A thermocouple whose junction can be approximated as a 0.5-mm-diameter sphere will be used to detect the temperature of a gas flow. The junction's characteristics are = 5535 kg/m3, cp = 314 J/kgK, and k = 32.5 W/mK. Between the junction and the gas, the convection heat transfer coefficient is h = 165 W/m2K.

a) Assess the solution available to analyse this problem b) Calculate the time constant of this thermocouple. c) Determine how long it will take for the thermocouple to read 99 percent of the initial temperature difference (e.g. when Tinitial junc = 0 C and Too = 100 C, time to reach Tjune = 99 C)