An office worker uses an immersion heater to warm250 g of water in a light, covered, insulated cup from 20.°C to100.°C in 4.00 minutes. The heater is a Nichrome resistancewire connected to a 120 - V power supply. Assume the wire is at100.°C throughout the 4.00 - min time interval. (a) Calculatethe average power required to warm the water to 100.°C in4.00 min. (b) Calculate the required resistance in the heatingelement at 100.°C. (c) Calculate the resistance of the heatingelement at 20.°C. (d) Derive a relationship between thediameter of the wire, the resistivity at 20.°C, ρ0, the resistanceat 20.°C, R0, and the length L. (e) If L = 3.00 m, what is thediameter of the wire?

An office worker uses an immersion heater to warm
250 g of water in a light, covered, insulated cup from 20.°C to
100.°C in 4.00 minutes. The heater is a Nichrome resistance
wire connected to a 120 - V power supply. Assume the wire is at
100.°C throughout the 4.00 - min time interval. (a) Calculate
the average power required to warm the water to 100.°C in
4.00 min. (b) Calculate the required resistance in the heating
element at 100.°C. (c) Calculate the resistance of the heating
element at 20.°C. (d) Derive a relationship between the
diameter of the wire, the resistivity at 20.°C, ρ₀, the resistance
at 20.°C, R₀, and the length L. (e) If L = 3.00 m, what is the
diameter of the wire?