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It is refreshing to take a cool shower in hot weather. And for the sake of discussion, lets assume that one should be "comfortable" with temeratures when taking a shower.

Considering that the vast majority of the heat from a shower is lost down the drain, would it not be more energy efficient to heat a confined space (shower stall) to a temperature that would allow you to shower with cool water rather than hot?

How hot would it have to be in the room for 70 degree water to be "nice." 60 degree?

And since all of the energy used to heat the air in the space would remain in the space/room, would you use less energy to take a comfortable shower doing it that way?

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    $\begingroup$ @CuriousOne - True, but this doesn't address the question. IF it turns out that heating the air WOULD yield energy savings, then one could compare the savings to those from reusing the heat in the draining hot water. And then there would be the question of cost of both solutions. $\endgroup$ – That Idiot Jan 25 '16 at 12:39
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    $\begingroup$ Apparently nothing stops you from snarky responses. I posted here because while the calculations are "rather trivial," to you, it would take me quite a bit of background research to do them. My hope is that the calculations would be so trivial to members of physics.stackexchange.com that I could get an answer without attitude. $\endgroup$ – That Idiot Jan 25 '16 at 12:43
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    $\begingroup$ If it is an answer, then it should be posted in Answers, not Comments. And quality Answers on Stack Exchange require more than someone saying "it does" or "it doesn't." So if you are going to answer the question, I request you show your work - or at least provide links to supporting info. $\endgroup$ – That Idiot Jan 25 '16 at 12:48
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    $\begingroup$ @CuriousOne Do you really think that radiation is the primary heat transfer mechanism from the body to the surroundings? If that were the case, then on a cold day, the presence or absence of wind would have negligible effect on your skin temperature. In my judgment (and experience) conduction and convection to the air are much more important than radiation. $\endgroup$ – Chet Miller Jan 25 '16 at 13:13
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    $\begingroup$ @CuriousOne With all due respect, I still contend that conduction and convection dominate the heat transfer. $\endgroup$ – Chet Miller Jan 25 '16 at 14:24
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Consider that the specific heat of water is 4.147 kJ/kg. The specific heat of air is less than 1/4 of that, so for the air to heat you as much as the water, you would have to heat the air to a much higher temperature. That's one reason, along with conduction, that Arctic explorers say that water cools you 30 times faster than air.

So it doesn't balance out. It's 4 times easier to heat air, but water cools you 30 times faster.

Even if this wasn't the case, your system would need to have a much higher temperature in it, which would mean more electricity, which would mean more electricity wasted in wires.

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  • $\begingroup$ So say the "steam room" shower stall was brought up to 110 degrees F at 100% humidity. And say the water from the shower covers 40% of the skin at any given time (total guess for lack of actual info). How cool would you guess the water could be while still maintaining standard body temp? $\endgroup$ – That Idiot Jan 25 '16 at 15:20
  • $\begingroup$ Well, I see a problem already. If you maintain standard body temp, the water will not feel refreshing or warm. It will feel (more or less) completely neutral. $\endgroup$ – DevilApple227 Jan 25 '16 at 15:26
  • $\begingroup$ Consider this: even in hot, humid weather, when it rains and the rain is cold, you can start getting cold. You certainly won't be enjoying a nice hot shower, even at 110 ºF, 100% humidity, and rain. $\endgroup$ – DevilApple227 Jan 25 '16 at 15:29
  • $\begingroup$ But it is very refreshing/nice to take a cool shower when it is hot out. I feel like you'd be no less comfortable showering with cool water when it is hot out than you would be showering with warm water when it is cool out. I suppose there is a lot of variation between personal tastes. I wonder what the relationship between ambient temp (or radiant heat input) and comfortable shower water temps is - there must be some predictable trend. In my steam room shower experience, I very quickly found that I didn't want the water hot. $\endgroup$ – That Idiot Jan 25 '16 at 15:42
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    $\begingroup$ So this would certainly ENHANCE your experience in a cold shower, because the relative temp would lower. (water temp relative to air temp). Notice: I said ENHANCE, not make cheaper. In the end, if you want a good cold shower experience you would do this, but you would burn a lot more energy. $\endgroup$ – DevilApple227 Jan 25 '16 at 15:51
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According to a steam shower vendor, a 10KW unit is required to provide enough steam at 118 deg.F in a 6'x8'x 8' enclosure. The timer runs for 20 minutes (about right for a nice shower), so figure the unit would use 3.3KW and 2 gallons of water to make the steam room hot and steamy.

According to numbers pulled from all over, figure an average 20 min shower uses 50 gallons of water (416.5 lbs.), and that in my area that water comes out of the ground at 55 degrees F. To heat that water to 110 deg.F would take approx 22,910 BTU.

Converting KW to BTU (and here are the limits of my understanding - please correct my conversions/assumptions as needed) it looks like 3.3KW is about 11,260 BTU.

If this is all reasonable, then heating the shower to 82.5 deg.F would require 11,500 BTU, which, when added to the 11,260 BTU for the steam would total 22,760 BTU - or slightly less than just running the hot shower by itself. If you could go with heating the shower water even less,then the savings would appear to increase.

I am fully aware that this answer is full of broad assumptions, simplifications, and perhaps misunderstandings.

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