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. Specify a diameter and a length the wire can have. Can it be made from less than 0.5 cm3 of Nichrome?

Question

Physics

Braeden Ali

20 May, 13:12

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. Specify a diameter and a length the wire can have. Can it be made from less than 0.5 cm3 of Nichrome?

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Mathew Blackwell · Answer 1

The amount of energy needed to raise the temperature of 250 g of water from 20 to 100 degree Celsius is

Q = 250 (4.18) (100 - 20)

Q = 83600 J

The power delivered is

P = 83600 / (4 (60))

P = 348.33 W

According to the data for a Nichrome wire, the wire gauge for power rating of 348.33 W and 120 V power supply is

23-27 AWG