Question

A family comes home from a long vacation with laundry to do and showers to take. The water heater has been turned off during the vacation. If the heater has a capacity of 50.0 gallons and a 4 800-W heating element, how much time is required to raise the temperature of the water from 20.0C^ { \circ } \mathrm { C } to 60.0C^ { \circ } \mathrm { C }? Assume the heater is well insulated and no water is withdrawn from the tank during that time.

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In this problem, water of volume V=50.0 gallonsV = 50.0~\mathrm{gallons} is heated by a heating element of power P=4800 W\mathscr{P} = 4800~\mathrm{W}. The water is heated from T1=20.0 CT_{1} = 20.0~\mathrm{^{\circ}C} to T2=60.0 CT_{2} = 60.0~\mathrm{^{\circ}C}. We calculate the time taken to heat the water.

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