Hero999

The ash can be recycled in to building materials.

Waste heat can be used to heat surrounding buildings in district heating systems.

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Nigel Goodwin

There has been, and presumably still is, lots of such research - and coal fired power stations are amazingly efficient - the heat lost in the cooling towers is only a relatively tiny amount.

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Hero999

That's not true, a typical coal fired power station is about 36% efficient, a supercritical plant is only 45%. The only way to make it more efficient is to use the waste heat for district heating.

http://en.wikipedia.org/wiki/Heat_engine

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Nigel Goodwin

But how much is wasted in the cooling towers!.

In my experience, you can't use the waste for district heating because the plants are usually miles from anywhere?.

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Hero999

A lot of energy is wasted in the cooling towers, often they use a river as a heat sink but the increased temperature can create problems with the oxygen being less soluble in the water which can kill fish.

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Nigel Goodwin

But only small in percentage terms for the running of the plant.

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Pommie

Hero,

Maybe you can explain something that has confused me for a while concerning the Carnot engine.

Carnot seems to take the view that a body at 100ºC has 373*x energy available. A body at 50ºC has 323*x energy available, therefore the most energy we can recover is the difference between the two.

Taking the above bodies, I can recover 50/373 (Delta T/T hot = 13%) parts of the energy available. However, to put the system back to it's initial state I only have to add back the energy I have managed to extract. That is, heat the hot body from 50ºC to 100ºC.

This seems like a 100% efficient system to me. I think the view that the energy available has a datum at absolute zero is flawed.

Mike.

Hero999

Nigel,
No, if it's not used to run a district heating system then most of the energy from the coal is wasted. A supercritical plant will waste 55% of the energy in the coal. There's nothing that can be done about it, the laws of thermodynamics limit the amount of work that can be done given a certain temperature differential.

What Carnot says is that the amount proportion of heat that can be converted to useful work depends on the temperature difference between the two bodies and their absolute temperature. The remaining heat energy goes in to heating up the cold sink and is wasted.

No, if you put back the amount of energy you've managed to extract. you will not heat is back up to 100ºC.

Think of a hydroelectic power station, the maximum efficiency is deturmined by the the pressure difference of the water on one side of the turbine relitive to the other side of the turbine which is deturmined by height of the dam. Not all the potential energe in the water can be converted to mechanical energy because the water will keep moving after it's been through the turbine.

The same is true for our heat engine, work is done by the heat flowing from a hot region to a cold region, it can't all be converted to work because the cold region wouldn't be warmed up and the flow of heat would stop.

Here's an example, we have an ideal heat engine an a litre of boiling water 100ºC on the hot side and room temperature 20ºC on the cold side.



The heat energy required to heat the water to room temperature is.

Given that it takes 4.2J to rais the temperature of 1ml by 1ºK.

The amount of useful work we can perform with our litre of boiling water is 0.2144*336000 = 72.04kJ.

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Pommie

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? 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). Where do the losses go in this case?

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 Carnots efficiency equation.

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.

Hero999

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.

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.

As always heating up the cold sink.

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.

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.

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Pommie

The heat pump example has convinced me that the basic concept is correct, however, should Carnot's rule be applied to steam or IC engines. As I can run a steam engine on compressed air and do useful work with no temperature differential, doesn't this show that Carnot's rule cannot always be relied upon to predict efficiency?

Mike.

Hero999

Carnot's rule only applies to converting thermal energy to another form of energy (be it mechanical, electrical or chemical) and to doing work to move heat from one place to another.

Carnot's rule doesn't apply to other energy conversion devices such as electric/pneumatic motors, transformers, hydrogen fuel cells and LEDs..

If you use compressed air to power a steam engine (in which case you could no longer call it a steam engine), the maximum theoretical efficiency will depend in the pressure differential between the input to the exhaust pressure.

All Carnot's rule says is that in order to convert heat to another form of energy you need a temperature difference, just like you need a pressure difference to power your 'steam engine' from compressed air. It's actually quite obvious when you think about it; it's just not always easy to visualise and that's why it isn't always easy to understand.

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Oznog

Well you need to look up not just the "energy" and "efficiency" content, but "entropy" and "enthalpy".

For example, a Stirling engine can take a mass of hot liquid or gas and
a mass of cold liquid or gas and make work out of it. However, if it has no cold mass, it cannot do any work. If I place it in a sealed tank of 300F fluid it can't work.

That's not a limitation of only the Stirling design. It's a limitation of ALL machines and processes. Think of it like having a tank of 100PSI air and an air turbine to generate electricity. If I lived on the surface at 14PSI, I could let the air blow through the turbine. It raises the pressure of the environment (though the environment being so huge it's an inconsequential amount). But if I try to install it in undersea research sub and the pressure outside is 100PSI, the pressure is the same and the air won't flow. We can only extract useful energy (work) through lessening the energy difference between two mediums. Sad too- I mean a refrigerator should MAKE electricity otherwise, shouldn't it? You're trying to take energy out of a box. But no, there's like 200 years of solid science on this one and it's as solid as the "energy is neither created nor destroyed" principle.

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