A 200-L electric water heater uses 2 kW. Assuming no heatloss, how long would it

Question

A 200-L electric water heater uses 2 kW. Assuming no heatloss, how long would it take to heat water in this tank from 23degrees Celsius to 75 degrees Celsius?
The answer is about 6.0 hours. Please showall work, in order to receive a rating of Lifesaver! Thank you somuch! :) A 200-L electric water heater uses 2 kW. Assuming no heatloss, how long would it take to heat water in this tank from 23degrees Celsius to 75 degrees Celsius?
The answer is about 6.0 hours. Please showall work, in order to receive a rating of Lifesaver! Thank you somuch! :)

Explanation / Answer

Because the density of water is approximately 1 g/L, we are tryingto heat up about 2 kg of water. Thus, using the formula q = mct, we want to find the amount of energy required to complete theprocess. q = (2 kg)(4184 J/kg-K)(75-23 K) = 4.35 x 103 kJ ofheat. Now your heater provides heat at a rate of 2 kW which equals 2kJ/second. Thus the time we require to heat up the water is givenby: (4.35 x 103 kJ)/(2 kJ/sec) = 2.18 x 105seconds. (2.18 x 105 seconds)/(3600 seconds/hour) = 6.0436 hours,which matches your answer of 6.0 hours.

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