Mechanical Engineering Question:

Required cooling involves calculating the heat leaks into the cooled space. This could involve solar loading, the heat leak through a wall or a window. Maybe the structural supports hold up a detector at cryogenic temperatures. Typically, you know something about how the amount of the heat leak varies with the temperature at its two sides. House insulation and windows have an R-value that tells you how much heat leaks through as a function of the internal and external temperatures.
Once you know the load, you can calculate the amount of energy required to provide that much cooling. An air conditioner sold in the United States will have an "Energy Efficiency Rating" that tells how many BTUs/hr of cooling are produced per watt of electrical power input. So if you need 5000 BTU of cooling and your A.C. has an EER of 10, you will need 5000/10 = 500 W of electrical power to run it.
In a country that uses a sensible unit system the cooling requirement and the electrical power, are both measured in Watts, so an A.C. will simply have a coefficient of performance (COP) which is the Watts of cooling per Watt of electrical power? COPs for typical air conditioners is about 3, so in the above example you would have calculated that you needed 1450 W of cooling, and with a COP of 3 you would need 480 W.