Pommie said:
Your using the equation/theory I'm questioning as proof!!
OK, I take a liter of oil at 20ºC and heat it to 100ºC. I then use a Carnot engine to retrieve the available energy. If it's only 24% efficient, where does the lost energy go? Heat? Sound? Movement?
That doesn't make any sense if we don't know the ambient temperature.
Alright, assuming from your 24% it's about 20ºC, the lost energy goes in to heating up the room.
If I then use 120ºC and 200ºC, why can I extract more? The energy added is the same (assuming non boiling liquid and an ambient of 120ºC).
What's the ambient temperature?
If it's 20ºC then you'll be able to extract a larger proportion of the energy.
If it's 120ºC, then no, the engine will be less efficient.
Where do the losses go in this case?
As always heating up the cold sink.
I'm not being flippant, I do believe that Carnot was referencing to absolute zero, and objects at room temperature hold vast amount of energy and this is why we can only recover a small amount. In reality, if we can recover the energy we have added we are vastly improving on Carnot's efficiency equation.
Alright, here's another way you can look at it, I'm not going to do any calculations on it but you can turn the whole thing on it's head. At the moment we've only being discussing heat engines, we haven't discussed the heat pump. Heat pumps move heat from cold regions to hot regions and as they're reducing the entropy they require energy. If we used a perfect Carnot heat pump to move heat from our room in to the water we could boil the water using only 74.04kJ.
How does this work?
Where does the rest of the energy come from?
The room!
Before we ran 336kJ of energy through our heat pump and extracted 74.04kJ as useful work, the rest of the energy was transferred to the room. We may have raised the room temperature by a couple of mK but it's not enough to make any difference as far as we're concerned.
Now we're doing 74.04kJ work to heat the water back up again. The extra energy has come from the room, we may have lowered the room temperature by a couple of mK but it's not enough to make any difference as far as we're concerned.
Heat pumps are used in real life to heat houses and office blocks, normally the air conditioning is just run in reverse so the outside is cooled down more and the inside is warmed up more. A heat pump might only use 2kW of electrical energy but deliver 6kW of heat energy to the room, the 4kW of extra energy comes from cooling down the outside more.
In real life both heat pumps and engines are less efficient than their Carnot counterparts which is why you can't get 100% efficiency in general.
To take your dam example, the dam should be much more efficient at 5000m to 4000m than from 1000 to 0 meters. This is exactly the same flawed thinking. Sea level is not the relevant datum, the lower level is. You only have to pump the water up 1000M to get back to status quo.
Mike.
You seem to have got a couple of things confused, the hotter the cold sink the less efficient it is.
To be picky sea level isn't really the datum, it's the ambient pressure at sea level.
In truth, I don't know how well my analogy compares to the heat engine/pump.
If it did compare well, if you put low pressure region in a perfect vacuum it would become 100% efficient. Come to think of it that makes sense, in practice you couldn't have a vacuum since there would always be molecules filling it from the high pressure region.
The same goes for our heat engine, if we put the cold sink at 0ºK our Carnot engine could run at 100% efficiency but in reality you can't get to 0ºK because heat from the warmer region will raise the temperature above 0ºK.
Another thing, please don't confuse work with energy, energy is all around us (in the form of heat) but we can't do anything with it. Energy gradients are the only thing that can do work and entropy (the inability to do work) always increases as the energy gradiants in a system even out.