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 4,000-W heating element, how much time is required to raise the temperature of the water from 20.0°C to 61.0°C? Assume the heater is well insulated and no water is withdrawn from the tank during that time.

50 gallons = 50 x 0.00378541

=.1892705 m³

mass of water = volume x density

=.1892705 x 10³

m = 189.27 kg

heat needed Q = m s Δ t

s is specific heat of water, Δ t is rise in temperature

= 189.27 x 4.2 x 10³x (61 - 20)

32592.3 x 10³ J

heating element will provide this energy. Let time taken be t.

heat produced by heating element with power of 4000W

= 4000 x t J

4000 t = 32592.3 x 10³

t = 8148 s

= 135.8 min

= 2 hour, 15.8 min.