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% o fthe final temperature within 5 s. Assume that the thermocouple's bead(its sensing element) is spherical with a density equal to 8000 kg/m^3, a specific heat at constant volume equal to 380 J/ (kg-K), and a convective heat transer coefficient equal to 210 W/ (m^2-K). Determine the maximum diamter that the thermocouple can have and still meet the desired response characteristics.