# Filling a bathtub (Hot water to cold water exchange)

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• archeryemily9085
In summary: When it warms up, it expands, and the pressure pushes the water up the pipe. This is why the cold water gets pushed into the hot water faster than the other way around.In summary, if you have limited hot water and you know someone just took a shower, it would be a better idea to first use all of it and add the cold water later, as the larger body of hot water filling the tub would make the cold water added later warm up faster.
archeryemily9085
TL;DR Summary
Hot water to cold water exchange
Hey there, I honestly don’t know if this is the right place for this, but I figured I would ask.

lets say you are going to take a bath, but someone just took a shower and you know your hot water heater will be running low on the goods.
Just for arguments sake, let’s say you have just enough hot water to fill half the tub, so a 50/50 split.
Would it be a better idea to first use all or most of the hot water and add the cooling/cold water later if the goal is to maintain the hottest bath you can? Or would that make the tub just as hot as if you filled the whole thing with equal parts hot and cold water from the start? Would the larger body of hot water filling the tub make the cold water added later warm up faster than if it just mixed in the pipe?

thanks again for the help, if this is indeed the right place for it!

Welcome,
archeryemily9085 said:
TL;DR Summary: Hot water to cold water exchange

Hey there, I honestly don’t know if this is the right place for this, but I figured I would ask.

lets say you are going to take a bath, but someone just took a shower and you know your hot water heater will be running low on the goods.
Just for arguments sake, let’s say you have just enough hot water to fill half the tub, so a 50/50 split.
Would it be a better idea to first use all or most of the hot water and add the cooling/cold water later if the goal is to maintain the hottest bath you can? Or would that make the tub just as hot as if you filled the whole thing with equal parts hot and cold water from the start? Would the larger body of hot water filling the tub make the cold water added later warm up faster than if it just mixed in the pipe?

thanks again for the help, if this is indeed the right place for it!
Welcome, @archeryemily9085 !

What do you think and why?

Could you use half-full tub with hot water only?

Well, I would like to preface this by saying that I am in no way a physicist, nor am I in school for anything related to this, so it’s kinda a stab in the dark. That said, I would think that if you use only hot water to begin with and let it run out half way full, the hot water accumulated in the tub would warm up the cold water added to it faster than the cold water cooled the tub water. I would guess that once the tub is full, even though there was just as much hot water added as cold, it would be warmer than if you added both in equal parts at the same time, and, in turn, adding the cold first would result in a colder bath at the end.
Like I said before, this is really just a gut feeling about something I know next to nothing about, so I’m not exactly making an argument here, but that’s what I had assumed.

My intuition is that you should add the cold water first, as long as you were sure of how much hot water you had at your disposal. If you added the hot water first, it would cool faster than the other way around, because of entropy and how evaporation works. Hotter things cool down faster than warm things, particularly water. I don't think it mixing in the pipe or in the tub would make a big difference as far as temperature goes, but it could affect temperature distribution until the water is well mixed. So for that reason and for convenience, I'd just have it mix in the pipe.

This is all assuming that your hot water would actually *run out* and not simply become less hot due to the water heater not being able to keep up. If the second is the case, just use all hot water which would then mix with the now warm water coming from the heater.

This is going to go around in circles with "yeah buts"

If it took zero time to fill, it wouldn't matter, right? You're mixing fixed amounts of water at T1 and T2 and it doens't matter which order, since it's instantaneous.

But it doesn't. If you put the cold water in first, it warms. If you put the hot water in first, it cools. So the question boils down to which happens faster. That depends on temperature, geometry, humidity, etc. I suspect in all practical cases, the hot water cools faster than the cold water heats, but this will get smothered in yeahbuts.

The water in the tank is also heating as the cold water is filling. so there's another universe of yeahbuts to explore.

nasu and Lnewqban
I'm a knucklehead. It doesn't matter which happens faster.

The cold warms. You want warming, not cooling. So the cold goes in first.
In that case, you have the heat provided by the hot water PLUS the heat from the environment. In the other order, it's the heat provided by the hot water MINUS the heat lost to the environment.

Last edited:
I'm a knucklehead. It doesn't matter which happens faster.

The cold warms. You want warming, not cooling. So the cold goes in first.
In that case, you have the heat provided by the hot water PLUS the heat from the environment. In the other order, it's the heat provided by the hot water MINUS the heat lost to the environment.
Yeah, but:
1. Cold water tends to be close to room temperature, so not much heat transfer in.
2. There's no way the heat loss rate of hot water in a tub is greater than the heat gain rate from the water heater.

Also "yeah, but": none of this is significant.

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