Hi,
Back in 2001 this very same question was asked and this was my reply. I admit it's a bit longer than it needed to be
Keep in mind this reply was directed to someone else who did a calculation and then wondered why it didnt work.
The question is based on two different topics:
1. efficiency
and
2. conservation of energy
On the one hand, your trying to measure efficiency, and
on the other hand, your using the 'answer' to decide
whether or not the air conditioner follows the law
of conservation of energy. The two are a little different.
Although it's correct to assume that no device should have
an efficiency of over 100% because it makes it look as though
it's not conserving energy, the calculation of this efficiency
is quite different depending on the dominate mode of operation.
What is efficiency?
Efficiency of a device that CONVERTS energy is the ratio of the
output power to the TOTAL input power, or
P(out)/P(in).
Efficiency of a device that TRANSFERS energy is very different,as
I'll show later.
In any case, this doesnt say anything about whether or not the
device conserves energy.
The formula for the conservation of energy law is:
energy(in)=energy(out)
The problem with your original calculation is simply that
for the purpose of calculating the efficiency of the device, the
input power is 600watts, but for the purpose of calculating
whether or not the device conserves energy (as it should),
the TOTAL input power is not 600 watts, or 2047BTU/hour...
that's just the electrical part of the input power.
The rest of the energy comes from the actual heat absorbed
on the evaporator side, which presumably is 5000BTU/hour in
a unit rated as such. This means the actual TOTAL input
energy (expressed in BTU/h) is really:
2047+5000=7047 BTU/hour
which is much higher then 600watts.
Now if you look at the output heat energy, you'll find very close to
7047 BTU/hour in the exhaust, as most of the heat absorbed
and the motor resistance heating and such are blown out by the fan.
In analyzing energy in and energy out, 7047 BTU in = 7047 BTU out as expected.
However you can still ask the question:
"How can 600watts(2047BTU/hour) of power provide 5000BTU/hour of
cooling, since a 600watt light bulb will only provide about
2047BTU/hour of heating?"
and the AC unit's efficiency seems way too high when you divide
5000 by 2047.
The answer to the mystery lies in the fact that
the principle mode of operation is not to
CONVERT
energy from one form to another, it's very different: it's to
TRANSFER energy.
The physical laws governing the transfer of energy are different than
the laws governing the conversion of energy from one form to another.
Recall that in conduction, the heat energy moves all by itself.
With the light bulb, 600watts of electrical energy are CONVERTED into
594watts of heat and 6watts of light(assuming 1% light to input ratio).
This is a very different process than trying to TRANSFER 5000BTU of
heat from one place to another, because it just so happens that there
are devices that have been constructed that can transfer much more
heat energy than the amount of energy input that they require in
order to accomplish this.
They are called 'heat pumps', and the air conditioner is just a heat
pump.
It should be obvious now that the decision of whether or not the air conditioner
follows the law of conservation of energy can't be made by measuring the
electrical input power alone. You can, however, obtain the efficiency in this
manner though.
The air conditioner efficiency is called EER which stands for
'Energy Efficiency Rating'. To obtain the EER of a particular unit,
divide the BTU rating (BTU) by the input power (watts). The aforementioned
5000BTU unit with 600 watt input would therefore have an EER of:
5000/600 = 8.3
which, by today's standards (10.0 minimum), is a little low.
A newer air conditioner would only consume about 500watts or less.
As a side note:
There is probably some very small amount of energy/mass lost in the process
contrary to Newtonian views, but it's so incredibly small it can't be
measured by todays standards--only calculated. It's probably on the order
of 1 part in 10 billion, so for all practical purposes involving air
conditioners, it can be ignored.
--Al