Question

What is the cost of heating a hot tub containing 1500 kg of water from 10.0ºC to 40.0ºC , assuming 75.0% efficiency to account for heat transfer to the surroundings? The cost of electricity is 9 cents/kWh .

Answer 1

E = K M ΔT energy required to heat water

M = 1.5E3 kg = 1.5E6 gm

E = 1 cal / gm C * 1.5E6 gm * 30 C = 4.5E7 cal

1 cal = 4.19 J

E = 4.19 * 4.5E7 J = 1.88E8 J

E(req) = 1.88E8 / .75 J = 2.51E8 J total heat required

1 kWh = 1 * 1000 J hr * 3600 sec / hr = 3.6E6 J

t = E(req) / E (input) = 2.51E8 / 3.6E6 = 69.7 sec

.09 / sec * 69.7 sec = 627 cents = 6.27 $

(Note 1500 kg = 3300 lbs or over 1.5 tons of water)