Question

A swimming pool heater has to be able to raise the temperature of the 40 000 gallons of water in the pool by 10.0 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. 1 960 kWh
b. 1 770 kWh
c. 330 kWh
d. 216 kWh

Answer 1

Answer:

b. 1 770 kWh

Explanation:

The heat needed to change the temperature of a certain amount of a substance is given by:

$Q=mC\Delta T$

Here m is the mass of the susbtance, C is the specific heat of the substance and $\Delta T$ is the temperature change

$Q=(40000*3.8kg)(4186\frac{J}{kg\cdot ^\circ C})(10^\circ C)\\Q=6.36*10^9J$

Recall that one watt hour is equivalent to 1 watt (1 W) of power sustained for 1 hour. One watt is equal to 1 J/s. So, one watt hour is equal to 3600 J and one kilowatt hour is equal to $3600*10^3 J$

$Q=6.36*10^9J*\frac{1kW\cdot h}{3600*10^3J}\\Q=1766.66kW\cdot h$