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Default Room in house is too warm, will adding a return air duct help the airflow in it?

Hi,

I have a room in my house that I use as an office that I have to keep the
door shut so the return air flow is very small. It has a 5/8" gap below the
2'6 door so I calculate this out to be around 18.75 sq.in. I have one air
vent in it and my *theory* is that I think is fed by a 6" flexible ductwork
of some type. This would be 28.27 sq.in. With my house set at 77 deg, this
room with the door open is usually around 81 deg. If I close the door which
is probably 12 hours per day, it rises to about 85 deg when the rest of the
house is 77 deg. I have a computer and a couple printers in it, so a few
things that generate heat.

The issue is that I am going to have to try and soundproof the room a little
better. I have a toddler that makes considerable noise and it can be
troublesome when I am working. I am going to get a solid core door and a
sweep for the bottom to cut off all the places where sound can enter
directly. This will however cut off the return air flow that I currently
have which doesn't seem to be doing the job.

My house currently has two return air vents both located in the hall way.
Each one is a 14x25, so 350 sq.in each or a total of 700 sq.in return air
flow. My HVAC system seems to be ductboard or some sort of flexble
ductwork. The ductwork that goes to all the supply vents is a round
insulated flexible stuff. The two existing return air vents look a bit
different in that they look like a constructed box tube. Silver foil on the
outside. I'm not sure if it is ductboard or something else.

Here are the things I have thought of doing, please recommend which is best:

1. Put in a vent that has nothing to do with the HVAC system, but is sort
of a room to room vent. I could pick another room that has decent enough
open space to one of the two main return air vents in the hallway. The
advantage here is that I wouldn't be doing anything on the HVAC system
myself. I am also providing a way for air to exit the room when supply air
wants to come in. I wonder however how well or not well this would work.
For some reason, it seems to me that even if I put in a large enough
vent/ductwork that it still wouldn't improve supply on my one supply vent.

2. Add a return air vent to my office. It looks like the smallest filter
that I can commonly find on the shelves at Lowe's is a 10x20. This would
add 200 sq.in. to my office for return air. Would this increase the airflow
I am getting through my single supply vent with the door shut? Would more
air being pulled out via the return vent push more cooler air in via the
supply? This would a nice feature if it worked out well. Are there any
downsides to this plan? I don't know if this is something I could do
myself, or partially do myself and then have the HVAC company that put the
system in come in and hook it up to the HVAC system.

3. Same as #2, but add a second supply vent in the office as well, doubling
it from 28.27 sq.in to 56.54 sq.in.

4. Are there any more issues with sound with either #1 or #2? I wonder if
#1 would be noisier because sound could come from the other room vent into
the office vent. I will probably be using the flexible ductwork like they
put in already so hopefully that doesn't transmit sound as well as something
metal might.

Thanks for any advice and help,

Alan