A windmill produces 1400 watts of electric power that is used to heat water. The efficiency is 100%. How long will it take to raise the temperature of 40 gallons of water by 50∘F?

3.5 h.

Explanation:

The heat required is given by;

Q = m * Cp * dt

where,

m = mass

Cp = specific heat

dt = temperature change

Remember,

Given,

Cp = 1 Btu / (°F. lb)

1 gallon of water = 8.35 lb

m = 40 * 8.35

= 334 lb

dt = 50 °F

Q = 334 * 1 * 50

= 16700 Btu.

Converting Btu to kWh

1 kWh = 3412 Btu

1 Btu = 1/3412 kWh

16700 Btu = 16700 * 1/3412 kWh

= 4.89 kWh

Power = 1400 watts

= 1.4 kWh/h

Therefore, time required to add 4.89 kWh at a rate of 1.4kW

= 4.89/1.4

= 3.5 h.