Does setting an air conditioner at a lower temperature ensure faster cooling than setting it at higher temperatures? Consider a situation where the temperature of the room is 40 degree C, then, if I set the temperature of the AC to 24 degree, lets say it takes 20min for room to come into the range of required temperature.
Now, if I would have set the temperature to 16 degree, will it still take only about 20min or will the cooling rate(dT/dt) be constant and time taken will be higher, possibly in the range of 30min or so?
If the cooling rate is a constant, is it really meaningful to set very low temperature since they result in releasing of more CFCs and are not even in the comfortable range.
 A: No, at least not for the standard types of AC systems used in almost all homes. These systems use thermostatic controls that are simple on/off switches, which means that reducing the setting of the thermostat in your example changes exactly nothing.
A: Often, yes.
It depends on the parameter settings in the control system for the AC and the maximum power of the AC. An AC with an inverter is able to adjust the cooling rate to arbitrary values. 
The power efficiency may be lower at high power. Additionally, occupants may prefer low noise to rapid cooling. The cooling rate may thus be partly dependent on the difference between desired and actual temperature ('Proportional gain'). 
The AC controller will often have an integral effect in addition, which will gradually increase the power so that it eventually reaches the desired point. This effect will also be dependent on the difference.
In your case, however, when the starting point is 40 degrees and the desired temperature is 24, the AC will probably run at maximum power from the start. The initial cooling rate will then be the same for both settings. 
A: The answer is no. A basic a/c unit like stated above is a simple on off unit with one blow setting. It will cool at the same rate reaching the temp you want no faster then setting it at the temp you want. The only way for this to be effective is for there to be different speed settings for the blower to increase the amount of air blown. Adding a fan to a room to help circulate the air will help most!
