I plan on getting a room air conditioner window unit as a back up unit to my central a/c system. I will mainly need the window unit for a room 13 x 26 (338 sq ft). Will an 8,000 BTU unit be enough for this size room? This will be used in the hot, humid southern Louisiana climate.

How many windows and what size? Double insulated?
How much insulation in walls?
How much insulation in ceiling?
Door size and placement? Outside? Inside?
Average mean summer temp?

This is the correct way to size a unit.

Now for a guess. 600 square foot per ton but in your case really hot and humid area I would figure 4 to 500 per ton.

8000 will be close but try to centrally locate the unit so it does not have to try and blow the cooling for 26 feet length.

You also will have to start the unit up sooner than the room will be used because of heat soak in the area has to be cooled and furniture. Everything holds heat and the unit has to work overtime during the first few hours of running in a hot room. Good luck.

The unit will blow air to the width of the room 12.5 ft. (room length is 26 feet). This is a living room/dining room area with an arch separating the two rooms.

The windows are double paned windows. "Low-emissivity ("E" Glass) means Energy - Efficient Windows WeatherGard windows will eliminate air leaks and "E" glass will reflect 40%-70% of the heat that is normally transmitted through clear glass."

DP Rated 55
R Value - 4.56, UV Block 75%, Solar Heat Gain coefficient .36, Center of Glass U Factor .22