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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.

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The air in the room has water vapor in it, and some of this water vapor condenses when it contacts the evaporator. Water vapor has a very high heat of vaporization, and this will affect the exit temperature of the air leaving the air conditioner.

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  • $\begingroup$ So this is basically the sensible vs latent cooling capacity distinction? If the output temperature were say 12°C (ΔT=15˚C), then only 50% of the rated power would be sensible cooling. From some random sources I found, it is typically more like 60-90%... Should I then expect that if it were hypothetically run in close-to-zero humidity, the output air would actually approach the -4°C mark? $\endgroup$
    – regnarg
    Jun 21 at 18:12
  • $\begingroup$ @regnarg, if the outlet air is colder than zero degrees Celsius, there would be a tendency for the evaporator coils to ice up. Due to that, I would expect the A/C unit to control its outlet temperature such that it would not get below approximately 5 deg Celsius. Practical considerations such as this lead to constraints that will not match up with your theoretical expectations. $\endgroup$ Jun 21 at 19:05

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