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The AC your landlord installed is rated at 8000 btu which is way too small for 900 sq ft. You need at least a 15000 Btu Air conditioner and a 'well insulated' house to be cool.
A good rule of thumb in the AC business says you need 1 ton (12000 btu) of Air conditioning for every 600 sq feet (if the house is well insulated) - if not - then you will need 1 ton (12000 btu) for every 400 sq feet.
So, if you have 900 sq feet and the house is well insulated you should have at least a 15000 btu unit.
If it's not well insulated you will need 24,000 btu.
It is a two ton system. and without doing a heat load Calculation and not knowing the heat load It would not be anything but a guess. But if everything is working properly and the system is clean and with good duct work, than it should be big enough for the size of your house.
Over here in my neck of the woods an apartment one bedroom would have a 1.5 ton unit, a 2 bedroom house 2 to 2.5 tons a 3 or 4 bedroom home would be a 3 ton or 3.5 ton. Without numbers no one can tell exactly what you have there. Figured i could give you an idea. If you have 8 foot walls go by a ton for each bed room in the house.
Lets look at the whole problem. Did you have a new unit inside. Is the charge correct for unit. 1 lb of refrigerant makes difference. Four tons should be big enough if you have proper insulation. I have three tons in a 2100 square foot house. Its plenty big enough. You may have to small a return air. To small a return can cut a four ton unit to 2.5 ton unit very easily. 1.5 square foot pf free grille area per ton. Rusty
That is a fairly large difference. It is usually ok to have the inside evap. coil and blower up to 1 ton larger than the outside condenser. That will make the unit slightly more efficient as well as less likely to freeze up on low airflow situations. It is not recommended to install a new condenser on an old evap coil. There has been a lot of changes to the design of the coils in the last little while. For example a 10 year old 2 ton coil may only have 3 cubic feet of volume but a new 2 ton coil may have 4 cubit feet of volume.
There are many factors that may have infulenced the decision on what size condenser to install. Many of which can only be done by visiting the home and doing alot of work, checking the duct sizing bioth supply and return, inspecting the insulation and windows of the home etc. etc. Most of the time that never gets done. You can blame the contractor for not doing a complete check, but at the same time you can blame the customer because many contractors that are that good loose the job to a cheaper bid that did not no any of the research. It is a catch 22 for everyone involved.
There is ALOT more to sizing equipment that many people think, sadly that also includes many HVAC contractors. Way too many people use "rule of thumbs" or flat out "guess".
Sorry for the rant but your queston can only be answered by a good well educated HVAC contractor visiting your home. That type of a contractor is getting hard to find these days in such a price competetive world.
I recently contacted Carrier Corp after our routine annual HVAC check on our residential system indicated that our 4 ton AC unit and 3 ton unit had leaking evaporator coils.
They basically told me to shove it in a very curt letter - In other words even though a leaking evaporator coil is a manufacturing defect they will not offer any financial assistance in replacing the failed evaporator coils.
I spoke to several HVAC engineers and they indicated Carrier has a high percentage of evaporator coils and compressor failures on residental HVAC systems.
The copper wall of the evaporator coil is being drawn thinner than in earlier years and the R22 being acidic slowly eats through the copper tubing.
Evaporator coils should not fail according to the HVAC Engineers if properly manufactured.