An office worker uses an immersion heater to warm 349 g of water in a light, covered, insulated cup from 20°C to 100°C in 2.00 minutes. The heater is a Nichrome resistance wire connected to a 120-V power supply. Assume that the wire is at 100°C throughout the 2.00-min time interval. (a) Calculate the average power required to warm the water to 100°C in 2.00 min. (The specific heat of water is 4186 J/kg · °C.)
W

(b) Calculate the required resistance in the heating element at 100°C.
Ω

(c) Calculate the resistance of the heating element at 20.0°C.
Ω

(d) Derive a relationship between the diameter of the wire, the resistivity at 20.0°C, 0, the resistance at 20.0°C, R0, and the length L. (Do not substitute numerical values; use variables only.)
d =

(e) If L = 3.00 m, what is the diameter of the wire?
mm