Worth leaving shower/bath water to cool down?

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Tendency here is to leave shower/bath water to cool down thus releasing its warmth to the bathroom. We always have the exhaust fan running while bathing of course to get rid of moisture.
And while we are in the bathroom (in centre of house, no windows) six 40 watts bulbs (total 240 watts) above the vanity mirror are on keeping the temperature comfortable so that relative humidity is not a problem.The mirror. for example, fogs over for five to six minutes and then clears by itself. There are no mould/mildew problems.
We have a fiberglass-shower tub unit. Hot water is heated electrically in basement below. A 500 watt baseboard bathroom electric heater rarely cuts in, the lights and other warmth keeping up the bathroom temperature.
At the end of a typical shower there is warm water in the tub about 4 inches deep, 15 to 18 inches wide and about 48 inches long. These are probably a bit overestimated; but to continue ............. that's 0.3 x 1.5 x 4 cu feet of water = 1.8 lets say 2 cubic feet of water?
Water weighs 'about' 60 pounds per cu foot. So 60 x 2 = approx. 120 pounds of soapy water at a temperature of around the human body; say 90 degrees F? . Leaving it to cool down for an hour or two, to say a room temperature of 70 degrees F releases 120 pounds times 20 degrees = 2400 BTUs of warmth.
One kilowatt/hr of electricity will produce 3300 BTUs of heat.
So 2400 BTU's of warmth requires 2400/3300 = 0.73 (approx three quarters of a kilowatt/hr).
Our electrcity costs, on average, ten (10) cents per k.watt/hr. So; by doing this am I saving some 7 to 8 cents per shower?
With an average of 1.5 persons in house one shower each per day = 365 x 1.5 x 0.08 = potential saving of $44 per year? Enough, maybe, for a magazine subscription?
Welcome comments, criticism, or advice whether I have dropped a decimal point (or other grievous error) in calcs.
And of course the above is probably a 'high' average. Many showers are quicker than that (less used water). While, for example washing one's hair couple of times a week, while showering takes an extra minute or so.
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What is the actual temp of water in tub, its already cooled from air a alot, How much water does it take to clean the scum buildup every week. Turning down the thermostat water temp, insulating pipes, and low flow head will save alot more. Ng is cheaper than electric where I live.
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Couple of comments.
Yes, you are saving money by leaving the water to cool and give off the heat you paid for. Rather than leave the exhaust fan on, leave the door open a few inches and you won't get the buildup of moisture and you won't have to blow out the heated air. Neither of my bathrooms have vents and it has never been a problem if you open the door a bit. If you are afraid of someone seeing you naked, run the fan. Assuming the water is left, the next person taking a shower has to step into the dirty soapy mess?
Next is the water in the tub. We spend very little time cleaning the tub as all the dirt and soap are washed down the drain with little residue. It seems to me that after sitting for a couple of hours, the soap scum and other assorted dirt is going to need cleaning. That adds to both water use and the cost of cleaning solutions. That, plus your time, detracts from the $44 a year.
FWIW, my electric rate is 19¢, but my water is heated with oil.
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On Sun, 15 Feb 2009 06:32:38 -0800 (PST), terry

    It depends on where you are, but where I am most of the winter calls for running the humidifier to keep the humidity up to about 40% to avoid static problems and to make it more comfortable at a lower temperature. I suggest not running the exhaust fan during the heating season for most areas. You will save even more that way. Just allow the bath room to air out by opening the door, during or after each shower.
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terry wrote:

inches of water build up from a properly-installed and functioning shower. It should run out about as fast as it comes out of showerhead.
-- aem sends...
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Thanks for the comments. Yes: The drain plug is deliberately left in until water cools down. The 'used' water remains in the tub for an hour or two. Then next time someone is in bathroom they whip out the bath-plug while washing their hands in the sink anyway, after say, using the toilet. Scum build up is not a big problem here; but could be depending on how 'hard' (dissolved minerals) the water is. Also certain shampoos and even soaps, contain colouring and on occasion they do cause a rim-line that is slightly blue, or green, orange etc. depending on the colouring of the product used. Personally I just use a simple white soap for everything. So a white scum line I guess! Also agree the extra work of cleaning down the bath tub (although it has to be done every so often in any case) may not be worthwhile the slight saving per shower. Thanks for all posters rational and thoughtful suggestions about humidity. We find the dry house comfortable in this damp above and below freezing climate, but the suggestion not to run the fan but leave door ajar, may be a good one. This 1970s wood frame house seems to run about 35% humidity at a temperature of around 68-70 F. We WILL run the fan for what one TV ad politely refers to as "Embarrassing personal odours"! Well; gee when gotta go, you gotta go! Right? Thank you. terry
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the heat lost through the fan opening when the fan is on and even when the fan is off is more then the heat in the water...
I agree with the other posters, the heat lost via the fan is more significant..
and in the winter, more humidity is a good thing.
Mark
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...My first thought was the energy saved by not allowing the heat down the drain is offset by use of the exhaust fan. Not using the fan is a good if your house is <50% humidity. A higher humidity makes it feel warmer on the skin. I'm not sure I'd want to deal with the tub ring, though.
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Phisherman wrote:

If RH is 50% in my house in winter, all windows will fog up. See typical outside temp. is -20C range. It all depends.
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terry wrote:

Very weird thinking!
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When possible, in the winter. I do leave my shower or tub water until the next shower, or tub. I figure I paid for the gas to heat the water, and those BTU I want to keep in my trailer.
--
Christopher A. Young
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And you spent way more than anything you saved using new hot water to clean the scum off the shower/tub walls and floor from leaving the standing water. Penny wise pound foolish.
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You mean a galon of water every week contains more BTU than 40 galons of hot water, every day? Amazing. I'm going to have to make this into a research project, and get published. Thanks for a great research paper subject, you goofball.
--
Christopher A. Young
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On Feb 17, 8:27 pm, "Stormin Mormon"

40 gallons of hot water every day for SHOWERS? You're kidding, right? Do you have the Dugger freaks living with you?
PLONK!
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Now, remember. You did mention bath water. A tub full of water is betwen 40 and 50 galons.
--
Christopher A. Young
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50 gal x 8 pints/gal x 20 degree drop in temp = 8000 BTU 8000 / 134000 BTU (per gal kerosene) = 0.06 or 6/100 if 1 gal kerosene = $4.00 den 6/100 gal cost a bit less den a quarter. Keep it up and someday u be buyin a new caddy wid it (year 3009) - Cappy
On Feb 18, 7:28 am, "Stormin Mormon"

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On Wed, 18 Feb 2009 19:40:03 -0800 (PST), Cappy

Kerosene is going for $1.65/gal in my area. The better benefit of keeping the water is the added humidity.
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On Feb 17, 8:27 pm, "Stormin Mormon"

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[snip]

Never mind the energy issues -- you need to find out what's clogging your drain!!
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On Feb 16, 9:07 am, snipped-for-privacy@milmac.com (Doug Miller) wrote:

If you want to get that anal about extracting 8 cents of heat from shower waste water, they do have heat recovery devices you could install in the drain line. It's basicly a heat exchanger that runs the exiting waste water past the incoming cold water that is going to your water heater. I doubt it's practical, worth the cost/trouble, etc but at least you don't have to stand in 4 inchs of water taking a shower.
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