A thermocouple is made up of a spherical bead bimetallic junction at the end of two very thin wires of different materials. For example, in a type-T thermocouple, a copper wire and a constantan wire, with wire diameters ranging from 0.5 mm to 0.025 mm, are fused together to make a spherical bead that is also of a similar order-of-magnitude diameter. For such a thermocouple, determine the appropriate diameter of the spherical bead junction so as to ensure a response time of less than 2 s (Ƭ_t ≤ 2 s) in water, which is at 40°C and has a convective heat transfer coefficient of h̅ = 80 W/m² K. Consider the bead junction to have properties of Cu, and to be initially at 150°C. Also, for the calculated bead diameter, what would be the response time in air at 40°C and h̅ = 10 W/m² K?