eli5 Why is it that when you change the water from tub mode to shower mode that the water comes out cold at first?
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Because the lines to the shower head still have water in them from the previous time the shower head was used.
Once that water is pushed out, you have the temperature water you selected.
There’s a small section of vertical pipe that tees off from behind the tub faucet. There’s a valve keeping it shut. When you switch to shower mode, you open the valve. The pressurized water coming from the water heater will force its way up the vertical pipe, but the pipe is full of water from the last time you had a shower. So first the old water that’s sitting in the pipe has to get pushed out of the way, and that water is cold (or at least, room temperature) because it’s been sitting in the pipe.
In addition to the other answers, the tub in my old house the water DID drain out from the shower head when you turned it off, you could hear it running down and putting your hand over the shower head would stop it.
But the water was still cooler when it came out, and I finally concluded that was because the empty pipe and shower head would have cooled off, and the hot water going up the pipe was getting cooled off by contact with the metal.
It is the same reason that when you blow your nose out one nostril then switch to the other more snot comes out. The lines are different at a specific junction.
The water from the water heater has to reach the shower head regardless if water is standing in the line to the shower head or not. There’s still water in the piping that has exited the heater and has cooled off. That water has to be pushed out of the way. And we have to think about whether the heater is above or below (in a basement) the shower.
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