Carnot efficiency, mathematical slight of hand

[Tom Booth]

[Tom Booth]

Suppose I said that if I lift up a ball and drop it on some device for extracting energy, then I can only recover the potential gravitational force that I put into the ball by lifting it up off the ground. I can measure the height the ball is lifted with a ruler.

I claim that my energy recovery device is 100% efficient, meaning that the device can extract all the gravitational energy put into any object that is lifted up and dropped onto it.

No problem there.

But suppose some stranger comes along and points out that in reality, gravitational force extends all the way down to the center of the earth as well as out into outer space above.

Who is this wise guy?

OK, I can agree with that. So what? What exactly is your point mister?

The stranger replies, "well, your calculations are wrong. Your so-called gravitational force, energy recovery machine is nowhere near one hundred percent efficient, as you claim. If it were really 100% efficient it could extract all the gravitational force acting on the object all the way from the moon down to the center of the earth.

Get out of here you bloody idiot, you're out of your mind. The object was never lifted up to the moon, and the machine is not located at the center of the earth, but if an object could infact be dropped from the moon down to the center of the earth, then my machine would be able to extract all that energy, it IS 100% efficient!

No, it isn't.

Yes it is!

No, it is not!

Is.

Not.

This is a foolish argument, however, it is exactly the situation we are in today when it comes to calculating the "Carnot efficiency" of a heat engine.

For example, if I run a Stirling engine on a cup of boiled water, the temperature difference between ambient temperature and boiling is about 20% of the the temperature scale, all the way down to absolute zero Kelvin.

So, if my engine utilizes all the joules put into the water to bring it to a boil and as a result the temperature of the water is reduced back down to room temperature, all the heat added having been completely converted to work, then my engine has a "Carnot efficiency" of only 20%..

Wait a minute. But the engine converted every bit of heat that was added to the water into useful work output. How can you say that it is only 20% efficient?

The stranger smirks and says, Sorry, but on the absolute temperature scale, your engine has only utilized 20% of the heat energy.

Yes, sure, but the water, before we added heat to bring it to a boil was already eighty degrees Fahrenheit. Eighty degrees is the starting temperature. the baseline. We raised the temperature to boiling and the engine used all that heat bringing the water back down to eighty degrees. This engine IS one hundred percent efficient.

No it isn't. To be 100% efficient your engine would have to bring the temperature of the water down to absolute zero.

That's impossible!

Exactly!



Don't be fooled.

[Tom Booth]