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The correct size air conditioner for a 2400 square foot house can ONLY be determined by calculating the heat gain of the home. Determining the total heat gain of the home is a comprehensive process that includes using data about walls, insulation, ceilings, doors, roofs, attics, ventilation, overhangs, windows, construction quality, appliances, people, geographic location, geographic orientation, actual exterior shading on the home, humidity, desired temperatures and duct systems. Installing a air conditioner that is too small will not keep the house cool. Installing a system that is too big will make the house very uncomfortable and cost more money to operate. House air conditions are sized in "tons of cooling". Typically house air conditioners range in size from 1 ton to 5 tons. Some homes need more than one system. Some air conditioner run in multiple speeds such as a "high" and "low" operation. As an example a 5 ton 2-speed unit might also run in a 3-ton size. A 2400 square foot home in South Texas might need a 5 ton system while 2400 square foot home in Canada might not need air conditioning at all. If this is for a new air conditioning system a qualified contractor should be able to show you the process he used to determined the size. Determining the size of a home air conditioner is not a process most homeowners can do.
4000btu
It depends on your location, shade, windows, and insulation. You should be able to find a local A/C contractor who will do what's called a J-load calculation. There are also online calculators that will give you a rough approximation if you have an idea of how good your insulation and windows are.
The only sure way to tell you is to do a heat load calculation on your 4200 ft2 home. Such things as windows, insulation values and other factors effect the size of the unit or units that you would need.
5000 BTU is a tiny amount of cooling - are you sure you don't mean 50,000 BTU? A 5000 BTU might give you a drop of 5 degrees C in a 6' x 8' office with no south facing windows, as long as the ceiling isn't too high. For a normal 10' square room, 12,000 BTU is a more reasonable starting point, then add more for sources of heat gain in the room.