Question

Water heater contains 51 gal of water. part a how many kilowatt-hours of energy are necessary to heat the water in the water heater by 25 ∘c?

Answer 1

To heat the water in the water heater by 25°C, it would take approximately 0.184 kilowatt-hours of energy.

Step-by-step explanation:

To calculate the energy required to heat the water in the water heater, we can use the formula:

Energy (kWh) = (mass of water in gallons) x (specific heat capacity of water) x (temperature change in degrees Celsius)

In this case, the mass of water is given as 51 gallons, the specific heat capacity of water is approximately 4.184 J/g °C, and the temperature change is 25°C.

Converting the mass of water to kilograms, we get: 51 gallons x 3.78541 kg/gallon = 193.18791 kg.

Now, we can calculate the energy: Energy (kWh) = 193.18791 kg x 4.184 J/g °C x 25°C x (1 kWh / 3.6 x 10^6 J) = 0.184 kWh.

Therefore, it would take approximately 0.184 kilowatt-hours of energy to heat the water in the water heater by 25°C.

Answer 2

5.6 kilo-watt hours
The specific heat of water is 4.1796 J/(K*cm^3) which means that in order to raise the temperature of 1 cubic centimeter of water 1 Kelvin, it takes 4.1796 Joules of energy. So let's start by converting 51 gallons into cubic centimeters:
51 gal * 3.78541 L/gal * 1000 cm^3/L = 193055.91 cm^3
Since the size of 1 Kelvin is the same as the size of 1 degree C, we don't need to worry about converting the temperature. 25 degree C increase is the same as a 25 K increase. So let's calculate how many joules we need.
193055.91 cm^3 * 25 K * 4.1796 J/(K*cm^3) = 20172412.04 J
20172412.04 J = 20172412.04 kg*m^2/s^2
20172412.04 kg*m^2/s^2 / 3600 s/h = 5603.447788 watt hours. 5603 / 1000 = 5.6 kilowatt-hours.