The Cost of a Guilty Pleasure

I know that taking a bath uses more water than taking a shower. I know this for a fact. Put the plug in while you're having a shower and note the water level when you're done, almost guaranteed the tub isn't even half full. From a green standpoint it's abhorrent that I prefer baths to showers, I know. However when I come inside after walking home from the bus stop in -35, a 5 minute lukewarm shower just doesn't get rid of the chill. It really doesn't. Enter long hot bath. I've been wondering for a little while what my baths are costing me though, seeing as during the middle of winter they happen much more frequently.

Excuse me while I geek out for a bit, I've been wanting to do this calculation for a while.

If you're looking for an easy metric unit reference sheet, I'd recommend using this: http://xkcd.com/526/ Geeky, somewhat tongue in cheek, and not necessarily 100% accurate. Perfect.

The temperature of cold tap water here is close to 10 degrees celsius. I wouldn't be surprised if it's colder than that right now, but I'm going to use this as my starting point. I like my baths somewhere around 43 degrees to start, which means the water has to be heated 33 degrees.

My tub, very crudely measured to bath water level, is approximately 40cm x 60cm x 135cm. I'm not going to take my body volume out of there, we'll just assume that I'm going to warm up the water at some point. This gives us a volume of approximately 0.32m3.

It takes 4.184 Joules of energy to warm up 1 gram of water by 1 degree celsius. 1 gram of water is approximately 1cm3. So, in order to warm up my bath water, I'm going to require: 

(0.32m3) x (1,000,000cm3/1m3) x (33C) x (4.184J) = 44,183,040J or 44.18 MJ

So now I know how much energy this is going to take. Kinda. This is assuming everything goes absolutely perfectly, and that every last bit of energy is converted into heat and goes directly into the water. As nice as that would be, it doesn't happen this way. My hot water tank is heated by natural gas, which isn't overly efficient. Lets assume my tank is 65% efficient.

44MJ / 0.65 = 67.69MJ

That's probably a little closer to what is actually being used to heat the water. My gas bill charges by the Gigajoule of energy. Not that they know the exact amount of energy I'm getting, they've just applied an average conversion factor to the volume of gas provided. Anyway, from my last set of utility bills:

$3.97/GJ for the gas itself
$0.53/GJ for the gas delivery
$0.23/GJ for the GST on the gas
$4.73/GJ for heat

$1.59/m3 for the water itself
$1.18/m3 to drain the water
$2.77/m3 for water

Apparently GST is charged on gas and electricity, but not water? Oh well. I'm only taking the variable charges on this, because I have to pay the fixed charges regardless of whether or not I take a bath. I'm also not taking the electricity for the bathroom fan into account, because I don't really feel like looking for the motor rating. That would mean actually finding the label! lol.

So my guilty pleasure is currently costing me:

(0.06769GJ x $4.73/GJ) + (0.32m3 x $2.77/m3) = $1.21

That's better than I was expecting. Cheaper than Starbucks, that's for sure. However, I can see how this would add up over time. Having a hot bath every day of the month rather than a quick shower? That's almost $40!

It's enough to make me think "I'll just have a shower tonight". Tomorrow, maybe not so much ;)