BTU

Never knew what BTU was until recently. It is an abbreviation for British Thermal Unit. It is a non-standard unit for measuring energy.

Anybody who ever bought a small window AC unit knows about the abbreviation BTU. On the box, it is written the amount of BTU the unit can deliver. It's a simplified commercial abbreviation done for ease of reading because it should  have been written BTU/h. I've got an older 100 dollars unit that has a stated capacity of 5000 BTU and a a newer one of 120 dollars of 5000 BTU as well. With a P3 Kill A Watt power consumption meter, they each show a consumption of about 450 W, with the thermostat on continuously which coincides with the consumption written on their label.

From Wikipedia.

"When used as a unit of power for heating and cooling systems, BTU per hour (BTU/h) is the correct unit, though this is often abbreviated to just "BTU"

1 watt is approximately 3.41214 BTU/h

1000 BTU/h is approximately 293.071 W"

Thus for a unit of 5000 BTU/h, if written correctly, the equivalent of power in watts would be 1465.355 watts.

There are other ways used to approximate the power usage of an air conditioner which involves  the efficiency of a certain device, but they don't differ a lot from the scientific formula.

"For example, a 5000 BTU/h air-conditioning unit, with a SEER of 10, would consume 5000/10 = 500 Watts of power on average."

Please note that here is used correctly, BTU/h.

But according to the conversion formulas from the other Wikipedia page

5000 BTU/h divided by 3.41214 = 1465 W

That is how much a 5000 BTU/h AC  unit should draw from the grid. Instead, it draws a little over 400 W.

In reality they feel like they output 5000 BTU, not 1500 BTU as it results from multiplying the measured power, 450 with 3.42, the BTU/watt ratio. I don't believe it's a case of false advertisement.

Then anybody can tell me where the mistake is?

I personally think there is no mistake, the AC, as its cousin, the heat pump are truly over unity devices (output more energy than input). Do they violate the laws of physics as we know them? No, because heat pumps move heat from one area of space into another though they can move more heat than energy the compressor uses from the grid. It may appear so if you isolate the cold and hot part of a heat pump and see them as closed systems but not if you see the system as hole.

They manufacture, sell and advertise and use them for decades without the Universe being thorn apart or anything.

Proposed experiment. Feed both ends of an AC unit like this into a Stirling engine that has an efficiency of about 50%. At a consumption of 450 W you would have 10000 BTU entering the Sterling engine (adding both cold and hot output which for a small compact AC is lost) and hook a generator to it and see if you can get in the end more than 450 (input) watts.