A straight cylindrical nickel wire of length 2.00 m and radius 0.40 mm is connected across an ideal 12 V dc power supply. The resistivity of nickel at 20 °C is 6.9×10−8Ω⋅m. The temperature coefficient of resistivity for nickel is α=0.0050°C−1. After several seconds, the wire reaches a uniform temperature of 120 °C because of the Joule heating caused by the current.
(a) Determine the initial resistance of the wire at 20 °C and the initial current supplied by the power source.
(b) Determine the resistance of the wire when it has reached 120 °C and calculate the corresponding current.
(c) Calculate the percent change in the rate at which electrical energy is converted to thermal energy in the wire between 20 °C and 120 °C.
(d) Use your results to discuss whether the wire will continue to warm up beyond 120 °C or approach a thermal equilibrium near that temperature. Base your argument on the interplay between electrical power input and thermal energy loss to the environment.