A swimming pool heater has to be able to raise the temperature of the 50 000 gallons of water in the pool by 12.0 C°.How many kilowatt-hours of energy are required? (One gallon of water has a mass of approximately 3.8 kg and the specific heat of water is 4,186 J/kg⋅°C. )
A)6.98E+2 kWh
B)2.65E+3 kWh
C)2.21E+2 kWh
D)2.65E+4 kWh
E)2.65E+2 kWh

Question

Quizplus · Accepted Answer

The total heat energy required to raise the temperature of the pool by 12.0 C° can be calculated using the formula:

Q = m*Cp*ΔT

where 
m = mass of water = volume of water * density of water 
= (50,000 gallons) * (3.8 kg/gallon) 
= 190,000 kg

Cp = specific heat of water = 4,186 J/kg⋅°C

ΔT = temperature change = 12.0 C°

Therefore, 
Q = (190,000 kg) * (4,186 J/kg⋅°C) * (12.0 C°) 
= 9,969,120,000 J

Converting J to kWh, we get:

9,969,120,000 J * (1 kWh / 3.6E+6 J) 
= 2.77E+3 kWh

Therefore, the answer is B) 2.65E+3 kWh, which is the closest option.

A Swimming Pool Heater Has to Be Able to Raise