Suppose that your morning shower is 7 minutes long and uses 4 gallons of water per minute that is a nice 102 F in temperature. How much energy (kJ) must be used to heat the water for your shower if the water coming into your house is at 60 F? The heat capacity of water is 4.18 J/g ·K and the density of water is 1 g/cm 3. The units are kJ.

change 60F to degrees C,and change 102F to degrees C, then subtract, and find the change in temp in C

Now, change 4 gallons to liters, then to kg.

heat=kgwater*specificheatwater*changeTemp

To calculate the amount of energy required to heat the water for your shower, we need to use the formula:

Energy (kJ) = Heat capacity × Mass of water × Temperature change

Let's break down the calculation step by step:

1. Calculate the mass of water used during the shower:
Since your shower is 7 minutes long and uses 4 gallons of water per minute, the total amount of water used will be:
7 minutes × 4 gallons/minute = 28 gallons.

Since the density of water is 1 g/cm^3, we can convert the gallons to grams:
28 gallons × 3.78541 liters/gallon × 1000 cm^3/liter = 106242 grams.

2. Calculate the temperature change of the water:
The water coming into your house is at 60 °F, and you want it to be at 102 °F.
Temperature change = Final temperature - Initial temperature = 102 °F - 60 °F = 42 °F.

3. Convert the temperature change from Fahrenheit to Kelvin:
To convert Fahrenheit to Kelvin, we use the formula:
Temperature in Kelvin = (Temperature in Fahrenheit - 32) × 5/9 + 273.15.

Initial temperature in Kelvin = (60 °F - 32) × 5/9 + 273.15 = 288.71 K.
Final temperature in Kelvin = (102 °F - 32) × 5/9 + 273.15 = 312.04 K.

4. Calculate the energy (kJ) required:
Using the formula mentioned earlier and the given heat capacity:
Energy (kJ) = 4.18 J/g·K × 106242 grams × (312.04 K - 288.71 K) / 1000 = 966.21 kJ.

Therefore, approximately 966.21 kJ of energy must be used to heat the water for your shower.