As you can see in the book exterior walls require 2 top plates to tie corners and intersecting walls togeather. Interior walls must match height of outside walls to support ceiling joists. Technicaly 1 top plate could be used for interior walls but studs would have to be different from those on outside walls. You can use 1 top plate for what you are doing.

The ceiling joists are already in place and are perpendicular to this new wall.

Just use a pressure treated sole plate where it is in contact with concrete and use double studs at the door openings.

I thought pressure treated lumber was not allowed in conditioned living space. The concrete floor has radiant heating tubes embedded in it, so the sole plate will be glued to the floor.

What building code are you using? The IRC requires sleepers and sills on slabs to be PT or be separated from the slab by an impervious membrane. That may be difficult if you are using glue.

It is separated by an impervious membrane.

You need pressure treated for slab contact. If you have the impervious membrane, then you don't have a glue to slab connection and the wall will not be stable. You need mechanical fasteners. You should have a diagram of the loops that shows the gap where the planned wall will go where the gaps were planned into the system, so that they could be mechanically fastened. You cannot retrofit an addition of walls into a room where the loops were planned for an open room, as the system will then be improperly laid out to balance supply and return loops.

The supply and return loops were installed with the new wall (and another new wall) taken into account. In fact, the whole basement has five loops in four zones. The new wall extends from one outside wall to the opposite one, a little under 16 feet away, so the top plate will extend all the way without any joints. However, the original builder said to only use glue; he did for some partitions he installed. Since this wall hasn't been built yet, I should get some pressure treated lumber for the sole plate. I was going to glue the membrane to the floor, then the sole plate to it, but I guess that changing to pressure treated would be better; as I said before, I thought it was not allowed. When I examined the partitions installed by the original builder, I noticed that the sole plates were definitely different so I guess they are PT.

The new PT is not green so the slight difference in color and grain is not immediately obvious but if you know that it is easy to spot it.

Geeze, they're partition walls. Glue n' go.

Even with radiant heating, I've had basement walls nailed into the floor with one inch nails. (But, then, I knew how deep the radiant tubes were.)

One top plate is fine.

When you build the wall, you have two choices - stick build it, where you put in the top and bottom plates and frame in each stud, or build the wall on the floor and tip it up - if you have the room. If you do the later, build it 1/2" short and then shim the top plate right above each stud. This makes things fairly easy.

I would do PT for the sole plate, and glue it as you indicated. I typically glue than put a few bolts / power driven nail in.

"You should have a diagram of the loops that shows the gap where the planned wall will go where the gaps were planned into the system, so that they could be mechanically fastened."

Back in Toledo, everyone got angry at a fence contractor that cut off the gas to several hundred homes with a backhoe. The contractor pulled out the map of the gas lines provided to him by the gas company. The gas company put the line where they pleased, not where the prints indicated. Could happen here easily.

You ever tried to pry a pressure treated 2x4 off concrete? It will usually break before it lets go.

Actually, Joseph, I have and yes, it does break (or at least splinter). This was the sole plate in an eight-foot wall where I wanted to put a door, and it was fairly difficult to scrape off all the splinters of wood and glue, but I got it done. When my GC came in for another job, he said "Hey, you got it off!"

^^ Multitool with scraper blade :)