# Mixing cold with hot water - How long does it takes?

Sometimes the bath for my baby is too hot, so I mix into it some cold water. I open a cold water stream and mix the water with my hand waiting for the temperature to drop.

But here is something that I don't understand. After doing a really good mix with my hand, I notice that the hot water is kept together. It's hard to explain so check out the image.

• Step 1: I fill the bath with hot water
• Step 2: I open the cold water to stream into A
• Step 3: I close the cold water
• Step 4: I mix the water with my hand

After mixing the water, I can make it that the hot water is in A and the cold water is in B. Don't get me wrong it's not as hot and as cold as it was at time 0. But still there is a meaningful amount of hot water in A, that is too hot for my baby and, there is a meaningful amount of water in B that is too cold for my baby.

And this is not the only strange thing. I also like adding a color-bath-drops(It changes the water color) to the bath to make it more fun for the baby. The color sink/mix with the water much faster then it takes for the cold water and the hot water to reach the same temperature.

So here is my question:

## Is it expected?

Can you perform a theoretical experiment in which we mix hot water with cold water and some material that changes the water color, and calculate under what circumstances the material will get evenly distributed in the water before the water temperature will become the same in all the places?

• You may have failed to note something relevant. What you describes seems unlikely. Aug 23, 2019 at 5:07
• But here is a possible avenue to explore: For the water to molecules to mix (color mixing in) without all of the thermal energy mixing too, the energy must be trapped in the hot region by something other than the water molecules. The molecules basically occupy all of the space, and the air above the bath is probably moved around just as much as the water when you mix it, but... Aug 23, 2019 at 5:10
• The bathtub may be absorbing some of the heat locally, storing it, and then releasing it locally over time. This explanation goes against my intuition about, uh, bathtubs, but it is the best explanation I can come up with. Aug 23, 2019 at 5:13
• The thermal diffusivity of water is about 0.14e-6 m^2/s, while the food colouring diffusion coefficient is about 5.75e-10 m^2/s (if I looked up the numbers right). So I would expect heat to diffuse much faster than colour; the colour would presumably track parcels of water even after they have changed temperature. Aug 23, 2019 at 9:08
• @fyodrpetrovich Can you please put your thoughts into an answer. It will be easier to respond that way. There are two weird things here. The ability to swipe hot and cold water without full thermal mixing and secondly have the color-mix be faster than thermal-mix. Note that those are tap water we are talking about. I liked your idea about the bath surface, but then it does not explain the thermal switch of locations. I feel like there is some electric power keeping the hot water molecules together. What do you think? Aug 23, 2019 at 12:52