How is this posslibe?

[BrownOut]

Sears has a 5,200 BTU window mount air-conditioner advertised **broken link removed** Scrolling down to "Power and Performance" specification, it says the current draw is 4.5Amps, cooling amperage for 5200 BTU/HR. But the math doesn't work out:

1J = 3600 Watt*Hr
1BTU = 1055J source

so
1BTU = 1055*1J/3600 = .29Watts

And so
5200BTU/HR = 1524Watts. minimum, not considering system efficiency.

But at the specified 4.5Amps, that's only 540Watts. Am I missing something?

 

[ModemHead]

I don't think it's an energy conversion problem. The 5200BTU is existing heat energy to be moved from inside the house to outside. The 540Wh is how much energy it takes to accomplish the move. It gets converted to additional heat, which hopefully also ends up outside the house.

 

[BrownOut]

Do you think you can remove a quantity of energy using a lesser quantity of energy to do it? Doesn't that violate the laws of thermodynamics?

 

[ModemHead]

Well, you have the 1524Wh of heat energy and 540Wh of electrical energy going in the system, and presumably 1524+540Wh going out the back side as all heat, so I believe that works out fine.

 

[misterT]

Well, you have the 1524Wh of heat energy and 540Wh of electrical energy going in the system, and presumably 1524+540Wh going out the back side as all heat, so I believe that works out fine.

Yes.. that works fine. My fridge heats the room with more energy than it takes in from the socket.. that is the reason why my food gets cold.

 

[duffy]

Do you think you can remove a quantity of energy using a lesser quantity of energy to do it? Doesn't that violate the laws of thermodynamics?

Imagine a robot arm that used .2 kwh to move a 1200° crucible with 100 kwh thermal energy. Or imagine a 5 watt pump that moves a gallon of gasoline in a minute - pump uses .083 kwh to move 33 kwh of energy. The amount of energy getting moved around does not directly relate to the thing moving it.

 

[BrownOut]

I think we're hunting the wrong coon here. An A/C doesn't just move a container full of energy around. Instead it extract it from its medium and infuses a different medium with the extracted energy. It transforms energy, something that requires at least as much energy as what is being transformed.

 

[Roff]

According to this **broken link removed**, The efficiency of a refrigerator (equation. 9.17), defined as heat extracted per unit amount of work, is typically ≈5. Air conditioner efficiencies are typically ≈2-3.

 

[BrownOut]

Ok that makes my head spin. I"m gonna need to read that a couple times.

 

[Roff]

Ok that makes my head spin. I"m gonna need to read that a couple times.

Yeah, me too. I don't pretend to understand it. I just found it.
I was lucky to pass Thermodynamics 50 years ago. When I was a little kid, we had a red Coca Cola ice box. I understood that.

 

[BrownOut]

Makes me wish I paid more attention in thermo when I had the chance I'll re-read it and get back to you.

 

[RCinFLA]

https://en.wikipedia.org/wiki/Heat_pump

A good example is a heat pump hot water heater. They takes about 500 watts to produce the equivalent of a 1000 watts direct resistive heating element. They don't have the fast recovery of a 4 kW resistive element but with a larger reserve tank with good insulation you can avoid using their resistive backup element, relying solely on heat pump exchanger. The warmer the garage or storage room they are located the more efficient they are.

All cooling air conditioners are heat pumps (not counting swamp coolers). A reverse cycle air conditioner is also a heat pump for heating. (versus just resistive heat strips for heating). Their heating efficiency drops off if outside temp get much below 40 deg F.

 

[crutschow]

Heat pumps transfer heat energy from one location to another (one location gets hotter and the other location gets colder), the process theoretically (100% efficient pump) is not creating new heat. Thus the theoretical energy required to do this is simply the amount of heat energy transferred times the temperature difference between the two locations. The energy transferred can therefore be much greater than the energy required to do the transfer. That is why a heat pump is much more efficient in heating a house or water than resistive electric heating. This, of course, does not violate any laws of thermodynamics.

 

[Diver300]

The maximum amount of heat that can be pumped depends on the temperature difference. The smaller the temperature difference, the more heat that can be pumped, so if an aircon unit is pumping heat from a building at 20°C to outside at 30°C, that is a very small difference compared to the absolute temperatures (293 or 303°K) so lots more heat can be pumped than the power that is used.

Keeping the temperature difference small is why the condensers are large. For instance, my car has to dump around 5 kW or heat in the aircon condenser, but that is the same size as the radiator that has to dump 80 kW of heat. The aircon is kept efficient because the condenser temperature isn't far above the outside air temperature. The engine cooling water is about 80°C above outside air temperature, so lots more heat can be lost from that radiator. Having a smaller aircon radiator would make it run hotter, so it the aircon would be less efficient, the pump would have to be bigger etc.

Where I used to work we had a cryogenic cooler that cooled to around -260°C, or 13°K. Because of the huge temperature difference between that and the cooling water at 300°K, that used 2kW of power to pump about 20W of heat.

 

[gerty]

Another thing to take into consideration: manufacturers have been overating thier products a lot in the past several years.
Case in point: Our county Rescue Squad bought a portable air conditioner (the type that you vent to the outside through a window). I don't remember the exact numbers, but it goes something like this, the unit is rated for 800 sq ft. The meeting room we put it in is roughly 500 sq ft. I went down and turned it on at noon time for a meeting scheduled at 6:30 pm.
Controls were set at max cooling. I was the 5th person to arrive for the meeting and the room was still very hot.
A call to the manufacturer yielded the statement that 800 sq ft was just an "approximation".
Also look at a generator, in large print you'll see 6,000 watts, in small print you'll see surge, 5,000 watts continous.

I have come to the conclusion that manufacturers will lie to you about anything. (rant off)

 

[BrownOut]

Thanks guys. You've convinced me that I was wrong to assume the outputs must equal the inputs. I'm still gonna read over the thermo chapter from the pysics book posted. I was supposed to learn that about 20 years ago, but I was goofing off.

 

[MrAl]

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

 

[colin55]

You can't divide: 5000BTU unit with 600 watt input would therefore have an EER of:
5000/600 = 8.3
Air conditioners have an efficiency of about 230%.

 

[MrAl]

You can't divide: 5000BTU unit with 600 watt input would therefore have an EER of:
5000/600 = 8.3
Air conditioners have an efficiency of about 230%.

Hi,

What are you talking about? I can divide 5000 by 5 and get 1000, divide 5000 by 1000 and get 5, divide 5000 by 500 and get 10, no problems.
The EER is not the efficiency, it's just the EER, or the more modern SEER. It is related to the efficiency, but not the actual efficiency. The rating was invented by the air conditioner people and appears in their performance rating documents for heat pumps.

 

[duffy]

Want another "How is this possible" kind of mystery?

Go look at the HP rating on your shop vac. It's not uncommon to find them rated 6 peak HP or more. 6 hp would be 4474 watts, or 37 A off a 120 Vac wall outlet which isn't rated for more than 20 A.

On more than one occasion I've had people come to me with a proposal that involved running a 6 hp motor off a wall outlet. I tell them they can't do it. They point to a shop vac and tell me I don't know what I'm talking about. &%@#!