#### 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 20.0$^ { \circ } \mathrm { C }$ to 60.0$^ { \circ } \mathrm { C }$? Assume the heater is well insulated and no water is withdrawn from the tank during that time.

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#### Step 1

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

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