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 

Tinit (beginning temperature) 60℉
Tfinal (final temperature)  110℉
Qw (velocity of water)  5 gallons/minute 
ΔT (change in time)  20 minutes 
ρw (density of water)  8 lbm/gallon 

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: 

Vw = Qw * Δt

click to check answer

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. 

Mw = Vw * ρw 

click to check answer

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 (?? ℉) = Tfinal (℉) – Tinit (℉)

click to check answer

⃤  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. 

BTU (???) =(800 lb) * (50℉) * (1 BTU/lb℉) 

click to check answer

40,000 BTU's 

lb's and ℉ cancel out so we are left with units of only BTU 

Is 40,000 BTU a lot of energy? Let’s find out through work! Work is equivalent to energy, and defined as moving a force through a distance. An example of producing work is lifting a weight that stores energy. We call this potential energy. Let’s pose an interesting and fun question? How much potential energy can we store by lifting a 5lb sack of potatoes by 5 ft? Theoretically, we could convert that potential energy to another form of energy and use it to heat our shower. Let’s have some fun and learn at the same time through an energy experiment. 

TEKS Standards
College Board Units and Topics