Course:PHYS100/showers vs baths
Showers vs. Baths
- Cameron Costley - 29726106
- Jennifer Deol-71189096
- Darren Suderman-70488085
- Ravina Binning - 82724105
- Alexa Creelman - 44833101
Topic
Baths and showers are both commonly used in daily life, each using different quantities of water and electricity. Noting the differences in consumption between the two allows consumers to be more environmentally and consumption friendly, and save money! Our goal is to investigate the difference, in the amount and cost of energy, between taking a bath and taking a shower.
Problem
We want to compare the environmental and financial impact of two means of bathing: taking a shower and taking a bath. Both bathing and showering are commonly used by many people, but which is more efficient( "greener" and financially benefical)? We will evaluate this based on the difference in energy used to heat the water.
Appropriate Physics
- The difference between water temperatures,
- The energy required to heat the water,
- The volume of water used.
Power (W) = Energy (J)/Time (s)
1 BTU = energy required to raise the temperature of 1lb of water by 1 degrees Fahrenheit
1 BTU = 1055 J
1kwh = 3.06x10^6 J
Model
In both models we will be measuring the amount of water used as well as the temperature so that we can determine the amount of energy used in both bathing and showering. The temperature of the bath will be taken separately from the temperature of the shower. Using the temperature and volume we can determine the amount of electricity used per shower/bath.
The hot water tank being used is a 270L electric hot water heater with a power usage of 4622 Kilowatt Hours per Year. The average price of electricity is $0.07/kWh in Vancouver.
Model 1: Showering
- The showers will be run for 15 minutes
- Temperature will be taken directly under the shower head to minimize heat loss
- Water will be collected from the shower head for 30 seconds, from this we can determine the total volume of water used in 15 minutes
Model 2: Bathing
- The bathtub will be filled to exactly 35gal
- Temperature will be recorded upon completely filling tub
Assumptions
- Shower does not have a tap, water comes directly from shower head
- Rate of water usage in shower is constant over the 15 minutes
- Water temperature is being heated from 55 degrees F to 105 degrees F
- A 15min shower uses 20gal of water
- A bath uses 35gal of water
- The rate of water usage is constant
- Both the bath and the shower will last for exactly 15 minutes (excluding the time it takes to fill the tub)
- Bath loses no water to leaking or spilling
- Hot Water tank is 270L and is heated by electricity
- Calculations are for a single person having one shower or one bath per day
Calculations
- Shower
20gal water x 8.3lb/1gal = 166lb
(pounds of water) x (change in temp of 50F)
166lb x 50F = 8300 BTU
8300BTU x 1055J/1BTU = 8756500J/1 shower
8756500J x 1kwh/3.60x10^6 = 2.43236kwh/1 shower
2.43236kwh/1day x 365 days/1year = 887.81kwh/year
887.81kwh/year x $0.07/kwh = $62.15/ year to shower
- Bath
35gal water x 8.3lb/1gal = 290.5lb
(pounds of water) x (change in temp of 50F)
290.5 x 50F = 14525BTU
14525BTU x 1055J/1BTU = 15323875J/1 shower
15323875J x 1kwh/3.60x10^6 = 4.25663kwh/1 shower
4.25663kwh/1 day x 365 days/ 1 year =1553.67kwh/year
1553.67kwh/year x $0.07/kwh = $108.76/ year to take a bath
Results Interpretation
- Shower uses 166 lbs of water/shower and to heat this amount of water over the entire year requires 887.1 kwh/year.
- Bath uses 887.1 lbs of water/bath and to heat this amount of water over the entire year requires 1553.67 kwh/year.
- Therefore shower consumes the least amount of water and energy therefore more 'greener' choice.
- Shower costs $62.15 to heat the water over the year.
- Bath costs $108.76 to heat the water over the year.
- Therefore the shower is a better financial choice over taking a bath since it costs less.
Conclusions
In this project, we assessed the energy and cost efficiency of taking a shower compared to taking a bath. We found that taking a shower is more energy and cost efficient, showing a 43% reduction in energy usage and cost. Over the course of a year (assuming a shower is taken every day), this accounts for savings of $46.61 and 665.95 kWh for a single person. So although baths may be more soothing and comforting, the greener and environmentally friendly option would be to shower.