An engineer is designing a product in which a copper wire will carry large amounts of electricity. The resistive heating of a 65-g copper wire is expected to add 580 J of heat energy during a 10-minute operating cycle. The specific heat of copper is 0.385 J g^-1 °C^-1, the density is 8.94 g/cm³, and the coefficient of thermal expansion is 16.6 μm m^-1 K^-1.

(a) What is the temperature increase of the wire? 

(b) What is the initial length of the wire, assuming it is a cylinder and its radius is 0.080 cm?

(c) By what percentage does the length increase because of the temperature increase?

(d) Do you think the engineer should be considering this expansion in the design?