Questions
As I was doing laundry yesterday, a thought occurred to me… how much does it cost (in terms of utilities) to wash and dry a single load of clothing?Being the obsessive person that I am, I knew that the question would continue to haunt me until I found an answer. So today I did some hasty calculations and came up with some satisfying figures. The results of my research are as follows…
Making the assumption that
totalCost = washerCost + dryerCost = (washerElectricalCost + washerWaterCost + washerGasCost) + (dryerElectricalCost)
I proceeded to obtain a copy of last month’s water, electrical, and gas bills for my place of residence. I determined the following information:
- unitElectricalCost = (total electric bill / KWH used) = $0.0943 / KWH
- unitWaterCost = (total water bill / gallons used) = $0.00921 / gal
- unitGasCost = (total gas bill / therms used) = $1.186 / therm
The electrical computations were fairly straightforward (assuming operation at maximum rated power dissipation)…
- washerElectricalCost = unitElectricalCost * washerPowerUsage * washTime = ($0.0943 / KW hr) * (1200 W) * (KW / 1000 W) * (0.5 hr) = $0.0566
- dryerElectricalCost = unitElectricalCost * dryerPowerUsage * dryTime = ($0.0943 / KW hr) * (3240 W) * (KW / 1000 W) * (0.75 hr) = $0.229
To compute the water cost, I used a worst-case assumption that the water level is high (17.6 gal). Thus, the result was
washerWaterCost = unitWaterCost * washerCapacity = ($0.00921 / gal) * (17.6 gal) = $0.162
To compute the heating cost, I used a worst-case assumption that the water is hot (106.5°F). I also assumed that there are no energy losses in the gas water-heater, and that the water heater is a perfect insulator, so that I could use the formula
gasHeatingEnergyRequired = waterSpecificHeat * waterMass * waterTemperatureChange = (4.18 J / g-°C) * (66719g) * (41.38°C – 26.11°C) = 4258580 J
to determine how much energy is required to heat 17.6gal = 66719g of water from room temperature (79°F = 26.11°C) to the “hot” temperature (106.5°F = 41.38°C). Then I was able to compute the gas cost…
washerGasCost = unitGasCost * gasHeatingEnergyRequired = ($1.186 / therm) * (therm / 105480400 J) * (4258580 J) = $0.0479
Thus, the total cost is
totalCost = (washerElectricalCost + washerWaterCost + washerGasCost) + (dryerElectricalCost) = ($0.0566+ $0.162 + $0.0479) + ($0.229) = $0.496
In other words, the total cost for doing a load of laundry is about 50 cents. My curiosity is now satisfied.
Posted: September 29th, 2007 under Engineering.
Comments
Comment from Jed
Time 2007/09/29 at 4:52 pm
Thanks Bethany. Good point! Turns out detergent and fabric softeners do indeed add a significant cost (resulting in almost a 50% increase in my estimated price-per-load).
After perusing some drugstore websites, I find that
detergentCost = ($5.49 / 32 loads) * (1 load) = $0.172
softenerCost = ($4.99 / 80 loads) * (1 load) = $0.0624
So the total cost is now up to
$0.496 + $0.172 + $0.0624 = $0.730
putting my official estimate at somewhere around 75 cents.
Comment from Anonymous
Time 2007/09/29 at 10:57 pm
Very impressive! No wonder laundromats stay in business – at $2 a load, plus detergent. Fortunately, my laundry bill is included in tuition…of course, they’re probably making a killing on that, considering I only do laundry once every 2 weeks. What can I say? I have a lot of clothes. 
BethanyH
Comment from jeff
Time 2007/09/30 at 7:49 am
Unfortunately, the cost of the first load is roughly four orders of magnitude greater than the cost of the second… (thus partially explaining the cost at laundromats).
Now, if only we could figure out how to skip that expensive first load and go right to the second… oh, wait, we already know how to do that!
Comment from Marty McClurg
Time 2007/09/30 at 8:29 pm
Just in case you didn’t know, the machine fills and empties twice for each load, once for the wash cycle and once for the rinse cycle.
Maybe you could figure a way to decrease the amount of time I spend doing laundry.
Comment from Jed
Time 2007/10/01 at 12:11 pm
Ah yes, the rinse cycle is another thing I overlooked!
So the water cost (and possibly heating cost) would be doubled, resulting in the new total
$0.730 + $0.162 + $0.0479 = $0.940
Aargh! Now we’re up to $1.00 per load!
Comment from Bethany
Time 2007/09/29 at 4:01 pm
So… while you may be satisfied with your 50 cents a load estimate, I am not. As far as I can see, you failed to include the cost of detergents, softeners, etc. in your expenses. I could imagine the price of these necessities upping the cost of a load of laundry by a significant percentage. Fortunately, this should be easier to compute than water/heating/gas expenses
But otherwise, I’m impressed!