I’m putting this here instead of GQ because even though hopefully there is only one answer I understand there may be other opinions.
My old hot water heater was corroded on the bottom and I had it replaced a couple of months ago. The new one has water coming out of the relief valve and tube. Not just a few drops. I’m estimating at least 2 gallons a week. I have never had one do this before.
What is causing this and how do I stop it?
Once those relief valves blow once for whatever reason they may not close up tightly again. The valve may have been faulty or you were over pressure legitimately, but that valve may keep leaking until it’s replaced. There are a lot of potential reasons for high pressure that blew the valve to start with.
Is this electric or gas? Is it fed from a heating coil in a furnace or boiler?
It’s gas. It’s not fed from the furnace.
Did the valve blow? Where is the water coming from?
Like is it coming from one of the intake or out pipes, or just at the relief valve?
Who installed the water heater? Was it a licensed plumber, a DIY friend, you?
If it is just the valve, I would definitely consider replacing it. If it was installed by a licensed plumber, it might be under warranty. If you or a friend did it, then you might be stuck.
Either way, hopefully it is a relatively easy repair.
2 gallons a week - is it just a slow continuous drip, or occasional blasts? If it’s a drip, then yeah, your new heater came with a defective relief valve. Call whoever installed it. It’s an easy fix, he just has to drain it enough to unscrew the new valve without getting water all over your floor.
If it’s an occasional blast, then your tank is overpressured and it’s doing what it’s supposed to. If that’s actually the case, you might need another new tank.
On the far left in the picture in link it’s coming out of the long tube running along the side from the pressure relief valve.
It does not appear to be continuous but I haven’t put in the time to experiment under different conditions.
Here’s a possibility to consider from “Ask This Old House” (Richard Trethewy).
He talks about water expansion when the water is heated. If the water has no place to expand to, it may come out the T&P valve. A small expansion tank is the answer to this problem.
You should give it a warning. If that doesn’t work, suspend it for a week. 
Water is an incompressible fluid. Any air in the water heater will compress or expand.
Somebody’s gotta say it – might as well be me. It’s not a hot water heater – it’s a water heater. You don’t need to heat hot water.
BTW & FWIW, I had the very same problem once, years ago. Expansion tank did the trick.
Why doesn’t this happen to all water heaters? Perhaps there is usually enough air in a hot water heater to deal with pressure changes.
It isn’t the water than expands in a captive air tank, it is the air above the diaphragm.
Reading around the web, it seems that water does expand when heated. Here’s an Inspectapedia page on Hot Water Thermal Expansion Rate (Hot Water Pressure Increase in Hot Water Tanks or Boilers) that discusses this.
Why don’t all water heaters do this? I imagine that if they all had a one way valve installed ahead of the heater (trapping the expanding water in the heater tank), they might all do it.
As it is, well systems already have an expansion tank, and I doubt most municipal water systems routinely install one way valves except as noted in the video I posted - a pressure reduction valve which also acts as a one way valve.
Perhaps I’m wrong on this.
Thermal expansion, the density changes, not the volume.
That is how well pumps don’t have to run all the time water is running. Air compresses in the tank and pushes the water out the faucet.
Huh?
Water heated changes density and volume. Prevent room for expansion, and pressure goes up. Heat the water enough and the T&P valve will release the excess pressure.
From my second link:
“Stated very simply, and assuming our water temperature starts at 4 C (it’s tricky below that number as you’ll read below), then for every degree C that we increase the temperature of one unit (any unit-volume measurement) of water, its volume (expressed in the same units) will increase by 1.0208 (cubic meters, gallons, whatever).”
and
“Thermal expansion in a hot water system refers to the increase in volume of water as it is heated. If the water system is closed (say by a check valve or a blockage) the result is an increase in water system pressure as well. In other words if we heat water in a closed container, pressure in the container will increase.”
Additionally, as temperature goes up, density of the liquid goes down, and volume increases.
This exchange is confusing. Are we talking past each other?
If you do have an expansion tank installed, they aren’t forever. Have it checked as part of your boiler/water heater checkups.
Let’s go for “essentially incompressible”.
Your example says that for each Celsius degree that water is heated, it expands by .02%.
From 4 C to 100 C, when it boils, water will expand by 100(.02) = 2%.
Hot water may not be hot enough and still need heating. So it’s not a water heater, and not a hot water heater, it’s a hot and cold water heater.
If we want to get picky about it, probably the only time it doesn’t heat hot water is the first time you fire it up. After that, the water should never get cool in the tank. Unless you have a tankless unit… 