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

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

$Q=mc\Delta T$

$Q=3.8\times 40000\times 4186\times 10$

$Q=63,627.2\times 10^5 J$

$Q=63,672.2\times 10^2 KJ$

$Q=1767.42 kWh\approx 1770 kWh$