A thermocouple is made by welding two dissimilar metals into a small spherical bead. The potential difference between the two legs of the termocouple is a measure of the average temperature in the bead. Suppose that you have a chromel-alumel thermocouple bead, with the following material properties: \[Rho]=2700 kg m^-3, k=100 W/(m K), Subscript[C, p]=400 J/(kg K). The thermocouple bead has a radius of 1 mm. It is to be plunged suddenly from room temperature into boiling water (100 \[Degree]C), and the heat transfer coefficient is 10^4 W/(m^2 K). Determine the response time of the thermocouple, by calculating how long it takes for the thermocouple bead temperature to be within 0.1% of 100 \[Degree]C, i. e. how long does it take for the thermocouple temperature to rise to a temperature of 99.9 \[Degree]C? Hint: This is a small bead so we might want to test to see if we can simplify the handling of this problem as we could do for a thin sheet of Aluminum, i. e. check to see if Newtonian cooling applies.