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A family comes home from a long vacation with laundry to do and showers to take....

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A family comes home from a long vacation with laundry to do andshowers to take. The water heater has been turned off duringvacation. If the water heater has a capacity of 49.1 gallons and a4610 W heating element, how much time is required to raise thetemperature of the water from 18.8Â°C to 62.1Â°C? Assume that theheater is well insulated and no water is withdrawn from the tankduring this time.

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4.2 Ratings (807 Votes)

specific heat capacity of water C = 4186 J/kg/^oC

Â Â Â Â Â Â Â Â Â Â Â Â capacity of water in heater = 49.1 gallons

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 49.1 x 3.785 = 185.84 litre

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 185 .84 litre of water = 185.84 kg

Heat required to raise the temperature from 18.8^oC to 62.1^oC

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â H = 4186 x ( 62.1 - 18.8 ) x 185.84

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â H = 33684206.19 J

power of heater P = 4610 WÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1 W = 1 J/s

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â t = 33684206.19 / 4610

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â t =7306.8 s

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â t = 7306.8 / 60 x 60

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â t = 121.7 min = 2 hr 2 min

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â t = 2hr 2 min

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