Question

What is the cost (in $) of heating a hot tub containing 1460 kg of water from 10.0°C to 40.0°C, assuming 75.0% efficiency to account for heat transfer to the surroundings? The cost of electricity is 9.00 cents/(kW · h). What current (in A) was used by the 220 V AC electric heater, if this took 3.75 h?

Answer 1

Here ,

mass = 1460 Kg

specific heat of water = 4186 J/(Kg degree C)

total heat needed = m * S * delta T

total heat needed = 1460 * 4186 * (40 - 10)

total heat needed = 183346800 J

Now , as 1 kW.hr = 3600000 J

total heat needed = 183346800/3600000 kW.hr

total heat needed = 50.9 kW.hr

as the efficiency is 75 %

heat needed = 50.9/.75

heat needed = 67.9 kW.hr

cost = 67.9 * 0.09

cost = 6.11 $

the cost of heating is 6.11 $

b)
let the current is I

as ENergy = V * I * t

67.9 = 3.75 * 0.220 * I

I = 82.3 A

the current used is 82.3 A