In a planned experiment, a thermocouple is to be exposed to a step change in temperature. The response characteristics of the thermocouple must be such that the thermocouple's output reaches 98% of the final temperature within 5 s. Assume that the thermocouple's bead (its sensing element) is spherical with a density equal to 8000 kg/m3, a specific heat at constant volume equal to 380 J/(kg. K), and a convective heat transfer coefficient equal to 210 W/(m2.K). Determine the maximum diameter [] that the thermocouple can have and still meet the desired response characteristics. The unit is millimeter.