The heating element of a coffeemaker operates at 120 V andcarries a current of 4

Question

The heating element of a coffeemaker operates at 120 V andcarries a current of 4.00 A. Assuming thatthe water absorbs all of the energy converted by the resistor,calculate how long it takes to heat 0.600kg of water from room temperature (23°C) to the boilingpoint.
min
The heating element of a coffeemaker operates at 120 V andcarries a current of 4.00 A. Assuming thatthe water absorbs all of the energy converted by the resistor,calculate how long it takes to heat 0.600kg of water from room temperature (23°C) to the boilingpoint.
min

Explanation / Answer

Power of heating element P = V i                                          = 120 V * 4 A = 480 W So, heat released in 1 s E = 480 J mass of water m = 0. 6 kg temp t = 23 oC boiling temp t ' = 100 oC temp differece dt = t ' - t= 77 oC Heta required to raise the temp of water from 23 oC to 100 oCis Q = mC dt               Q = 0.6 * 4186 * 77= 193393.2 J So, required time T = Q / E                               = 402.9025 s                              = 6.715 min

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