Question

A swimming pool heater has to be able to raise the temperatureof the 40,000 gallons of water in the pool by 10 degress Celsius.How many kilowatt-hours of energy are required? (one gallon ofwater has a mass of approximately 3.8kg and the specific heat ofwater is 4186 J/kg C)

a.) 1960 kWh
b.) 1770 kWh
c.) 330 kWh
d.) 216 kWh

Answer 1

Answer:b)1770 kWh

Step-by-step explanation:

Given

volume of water
`V=40,000 gallons`

Temperature rise
`\Delta T=10^(\circ)C`

`c=4186 J/kg-^(\circ) C`

also 1 kg mass is approximately is 1 gallon

therefore 40,000 gallon is equivalent to 3.8\times 40000 kg

heat Required to raise temperature is

`Q=mc\Delta T`

`Q=3.8* 40000* 4186* 10`

`Q=63,627.2* 10^5 J`

`Q=63,672.2* 10^2 KJ`

`Q=1767.42 kWh\approx 1770 kWh`