# Air conditioner cooling capacity vs air flow rate and output air temperature

I have a Sinclair AMC-15A portable single-unit air conditioner. It's specifications state the following:

Cooling power: 4.4kW
Inside air flow rate: 420m3/h (max.)

This seemingly defies (my understanding of) physics. My model is the following: Cooling power is the amount of heat removed from the room (a decrease in the room's total heat energy) per unit time. Thus this should remove 4.4 kJ of heat every second it is running.

During this same second, 420/3600 = 0.117m3 or about 0.14kg of air goes through the cool air circuit. Basically, 0.14kg of air at some temperature $$T_1$$ (the original room temperature, say 27°C) is removed from the room and replaced with 0.14kg of air at some lower temperature $$T_2$$ (the temperature of the output air from the air conditioner).

Thus a different way to express the heat removed should be using the calorimetric equation:

$$Q = mc\Delta T$$

Where $$m$$ is the mass of the air (0.14kg), $$c$$ is the specific heat of air (approx. $$1 kJ / (kg\cdot °C)$$) and $$\Delta T$$ is the change to the temperature of this 0.14kg chunk of air. And we know the removed heat based on the calculation above should be 4.4kJ. When we plug all of this in and solve for $$\Delta T$$:

$$\Delta T = \frac{Q}{mc} = \frac{4.4 \rm{kJ}}{0.14kg · 1 kJ/(kg·°C)} = 31.4°C$$

From this I would conclude that to achieve the stated cooling effect, the output air would need to have a temperature of $$27 - 31.4 = -4.4°\rm{C}.$$ Which it clearly does not have (and should not have, considering human comfort).

This seems to be a contradiction. I presume there is some important error / omission in my understanding, but I cannot see where.