Office Air Conditioning and Open Windows Today is nice and sunny and the air con is on in the office. It's a fairly large office seating 20 people, 30x30x15ft with 20 small windows and a single large AC unit on the back wall where there are no windows about 12ft up. It blows air diagonally downwards and in front of it. 
It's about 25 degrees Celsius in here and the AC is set to 19, outdoors it is about 15 degrees. 
My question is:
If I open the windows do I contribute towards cooling the room or am I making it harder for the AC to reach optimal temperature?
My instinct tells me that because it's cooler outside than inside, by opening the windows It helps in cooling the room. Others think that opening the windows lets all the cooled air out. 
Which way does it work? 
 A: There is probably a lot more to this if you consider drafts and air turbulence, but lets keep it simple. Since the warmest place is in the building I would think opening the windows would only help with the cooling. Either it would let hot air escape, or let cold air come in. Sounds like a win-win.
Now if you want to consider humidity that a whole nother ball game.
A: According to the Second Law of Thermodynamics, heat flows naturally from an object at a higher temperature to an object at a lower temperature. 
This being said, if it is cooler outside than inside, you will contribute to the cooling of the office. However if it is humid outside, then there will be a relative humidity indoors. This can make it feel warmer than it actually is if there isn't enough airflow within the office. So if you open a single window in a corner of the office versus open a window on each side of the office, the latter will produce more cooling. 
Generally when it is cooler outside, turn the A/C off or roughly equal to the outside temperature (so that it turns itself off and doesn't turn on every 15-30 minutes). Save some money.
A: This is not a simple problem to solve for mathematically.  To do so you would need to know the temperature and velocity of the air coming out of the AC unit, as well as the velocity of air outside as well as which windows are open and at what angle outside air is hitting the windows.  Basically, you would need to figure out how well the AC air mixes with the room air as well as the the general paths the air currents follow.  
As others have mentioned, humidity is also a concern.  If you are bringing in humidity from the outside the AC will have to work harder to remove it.
For example, if the air from the A/C follows a laminar flow and does not mix well with the air in the room right away, a large part of it could goes out the window without having reduced air temperature.  The larger the temperature differential between the AC air and the room air, and the lower the amount of mixing occurs, the less efficient it is going to be.
Most likely it would be easier to just perform some experiments, trying to control for a single variable at a time.
However, having said that, assuming sufficient mixing of the air what you are going to see in practice is that opening the window causes the temperature to cool faster, because you have two sources of air colder than the room.  You could set up an equation using two idealized heat transfers to try to approximate it.  But if the temperature differential is only 4C you may find it doesn't really cool that much faster, and things like wind gusts and humidity may make it a wash.  In my experience, latent heat from the structure itself makes it very difficult to bring room temperature that close to outside air temperature (for instance, in a brick/stone wall type building I have found it difficult to cool an interior to closer than 5C above outdoor temperature over the course of a night).
However, in any case using both the AC and opening the windows will obviously use more electricity than just opening the windows. 
