Energy Excursions

# How Much Energy is Required For a Hot Shower?

How much energy is required to heat enough water for a twenty minute shower? Before we begin the exercise we must collect all of the data. Let’s say these are the typical parameters for a Texas high-school student taking a twenty-minute hot shower:

Tap water temperature = 60℉

Hot water shower temperature = 110℉

Shower head rate = 5 gallons per minute

Student’s shower time = 20 minutes

Now that we have the data, how much energy do we need for a single shower? We must solve for the required energy measured in BTUs to heat a 20 minute shower. Use the chart below for the relevant information we will need in order to calculate (1) amount of water in pounds (2) change in temperature in degrees Fahrenheit and (3) BTUs needed

Don’t forget the “physics!” It takes 1 BTU to heat 1 lb of water by 1℉.

1 BTU / lb * ℉

## Step One: How much water will we need?

First, let’s calculate the amount of water required for a 20 minute shower in pounds (lbs). Qw, Δt, and ρw are given in the table above. However, we first must find volume (Vw) using the equation:

#### 100 gallons

Vw = 5 gallons/minute * 20 minutes = 100 gallons

Minutes cancel out and we are left with gallons as our unit

Now that we know how many gallons are required, what about the mass of the water? You may remember the standard formula for mass: volume * density. Use the equation below to determine the mass of water (Mw) and check your answer before moving onto step two.

#### 800 lbm

Mw = 100 gal * 8 lbm/gal

gallons cancel out and the leftover unit is lbm

## Step Two: What is the change in temperature?

We know the temperature of the water prior to and after the standard twenty minute shower, but what is the change in temperature? Use the equation below and check your answer before moving onto the final step, calculating the BTUs required.

#### ⃤  T (50 ℉)

Tfinal (110 ℉) - Tinit (60 ℉)

## Step Three: Final Calculation

Here we need to calculate how many BTUs are required to heat 800 lbs of water by 50℉. Use the equation below and check your answer to see how much energy we need for a hot shower! Remember when using the equation, cancel out units that appear on the same side of the equation.