A Carnot engine between the Earth's poles and equator

Summary:
I am interested in a feasibility analysis of running a Carnot engine between poles and equator.
Earth absorbs and releases a massive amount of energy as a part of the day night cycles.(~100 Peta watts of solar radiation received) And the temperature difference between the poles and equator drive weather phenomenon, which happens at an energy scale beyond technology.

I am wondering if one can run a Carnot engine between from the pole to the equator. I am thinking of it as a massive infrastructure project, capable of meeting immediate energy needs of the planet.( Capable of generating atleast 5-10 terawatts of sustained power)

Here is a plausibility analysis, with some design choices (but feel free to design it differently).
1. I am thinking of using water for the required thermal mass. Water is abundant and has a high specific heat.
2. Water is contained in 2 seperate tubes, one for hot side and one for the cold side. The tubes run from poles to equator. The tubes are constructed using a non corrosive thermally conductive metal and surrounded by thick insulation.
3. On the hot side, I am imagining simple solar concentrators to keep the water above 90 degrees. On the cold side, I am imagining a simple heat exchanger keeping the temperature below 10 degrees. Solar concentrators and heat exchangers have a very long life span and recyclable. I chose the number 10 degrees and 90 degrees because it seems broad enough to be useful, and not so extreme that it would be difficult to maintain the temperature.
4. I will do my calculatation per Terawatt. 1 Terawattday = 8.64e+13 Joules. Using this we can get an estimate of the thermal mass of water required. 1 Terawatt day/(Specific heat of water*50 degrees) = 400 million Kgs of water. The temperature difference of 50 degrees is a crude choice. This is affected by efficiency and ability to maintain the temperature differences.
5. An ideal engine operating between 0C(273K) and 90C(363K) has an efficiency of about 25 pc. I am assuming in practice we can achieve an efficiency of 10 pc. So I will multiply the thermal mass by a factor of 10 and 4 billion Kgs of water. To be on the safe side we can estimate the amount of water required 10 billion Kgs/terawatt. But well within the realm of possibility.
6. It can be easily built in a modular fashion.

Some other similar design ideas,
1. Use different material for thermal mass, instead of water. One can consider some kind of molten salt, to keep the hot side at a very high temperature, but it becomes close to some designs of concentrated solar power plants. And it does not seem useful(except perhaps for efficient gains), and water is abundant.
2. Heating and cooling form a large part of residential energy use. It is possible to directly transport heat, But last mile delivery seems tricky.
3. Another way is to completely do away with water and just use a insulated conducting material to transport heat. But that looks very expensive.
I am wondering if such a design is feasible

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Staff Emeritus
Isn't it simpler and easier to take advantage of the natural thermalizion - wind and hydro?

bob012345, Astronuc and russ_watters
Drakkith
Staff Emeritus
I am wondering if such a design is feasible
Nothing is feasible when the scale is so large. Not yet at least.

DaveE
Gold Member
Building pipelines all the way to the equator to cool to 10C is a lot of effort when you could cool down to 40C or less at the equator. How would your system compare to in situ thermal-solar power plants?

Isn't it simpler and easier to take advantage of the natural thermalizion - wind and hydro?
Perhaps, but I wanted to evaluate it.

Building pipelines all the way to the equator to cool to 10C is a lot of effort when you could cool down to 40C or less at the equator. How would your system compare to in situ thermal-solar power plants?
Concentrated solar power is a very promising direction.

While writing this post I realized there is a fatal and unfixable flaw. I had overestimated heat flow capacity of metals by many orders of magnitude. If you want to generate terawatt scale power, then you would need to transport terawatt scale heat from equator to poles.

Copper conductivity is 386 W/m/K. If we have to transport 1 terawatt heat over 10000Km, we would require material of unimaginable conductivity.

russ_watters
Mentor
While writing this post I realized there is a fatal and unfixable flaw. I had overestimated heat flow capacity of metals by many orders of magnitude. If you want to generate terawatt scale power, then you would need to transport terawatt scale heat from equator to poles.

Copper conductivity is 386 W/m/K. If we have to transport 1 terawatt heat over 10000Km, we would require material of unimaginable conductivity.
I don't understand what you are getting at there. I thought your working fluid was water? Why do you need thermally conductive pipes? Seems to me you need un-conductive/insulated pipes.

What I'd be concerned with for this idea are:
• Construction cost.
• Pumping energy requirements.
• Heat loss on the journey.

Staff Emeritus
Well, also this takes all the energy out of the hydrological cycle. If you want weather, you will need to create it.

Baluncore
I would look at the cost of insulating a 10 Mm length of pipe.
Might you make a smaller version work between sea level and high altitude, on the steep windward face of a mountain range.

Astronuc, Keith_McClary and russ_watters
Keith_McClary
Gold Member
Might you make a smaller version work between sea level and high altitude, on the steep windward face of a mountain range.
In many places the air temperature is seasonally much greater or less then the ground temperature.

I don't understand what you are getting at there. I thought your working fluid was water? Why do you need thermally conductive pipes? Seems to me you need un-conductive/insulated pipes.

What I'd be concerned with for this idea are:
• Construction cost.
• Pumping energy requirements.
• Heat loss on the journey.

I wanted to use water as thermal mass, I did not intend to flow it, because it would be very expensive. I imagined the pipes had conductive layer followed by a insulating layer.

For a rough estimate for every KG of water pumped from equator to pole can store maximum of 4200KJ (100 degrees temperature difference). Which is a measly 1.2 KWh.

I had implicitly assumed conduction will be fast enough. But I realized I was many orders of magnitude away.

I don't think it is a fixable idea anymore.

@Prathyush Now I might be wrong but I think the main problem is not so much technical as it is physical. You see a thermodynamic system's efficiency and power output is directly dependent on the difference in temperature between the "hot side" and the "cold side" as well as the maximum temperature at the hot side. I think you might have heard that designers of steam generators and power plants always try to maximize the outlet maximum temperature.
A typical nuclear plant of the PWR style I think has about 300 to 350 celsius output @Astronuc surely knows more precisely.

In your proposed system the water doesn't even reach 100 degrees c which you get in your home kettle.
Also given the length of the pipe system , how much energy will be spent by pumping that water up and down? I think quite a bit.

Also the reason why the earth seems to get that much energy from the sun in total numbers is because of the large area that the sunlight covers , the problem is that this energy is spread out and mild and not focused , for energy production it is always better to have a focused source of energy. This is the reason why solar panels take up large areas simply because even though the total energy received from sun is huge but such is also the area that it is received upon.

I would look at the cost of insulating a 10 Mm length of pipe.
I don't know about costs but you can make a rough estimate for heat loss over 10000 Km.

If you assume the pipes are 20 m in circumference. And you use a material like styrofoam and use 1 meter thick insulation.
You get an estimate of 6-7 Gigawatts of power lost per degree of temperature difference. Heat losses are significant.

wow a 20m circumference for a pipe , that is more like a tunnel and less a pipe. I think you see it yourself @Prathyush this is unrealistic

@Prathyush this is unrealistic
Yes, I had said so myself. It cannot be made to work. I was just exploring the idea.

I was willing to sacrifice efficiency if most of the system can be made from passive elements, except the turbine but that is also not possible.

@Prathyush this is unrealistic
But I want to be clear it is unrealistic mainly because heat transfer from poles to equator is very expensive. You cannot do it passively, you need an active mechanism like motion.

russ_watters
Mentor
I wanted to use water as thermal mass, I did not intend to flow it, because it would be very expensive. I imagined the pipes had conductive layer followed by a insulating layer.
That makes no sense. If relying on conductivity the water would have to be conductive. Otherwise, why even have the water? I don't know what you think "thermal mass" means, but that isn't it.
I don't think it is a fixable idea anymore.
Agreed.

Astronuc
That makes no sense. If relying on conductivity the water would have to be conductive. Otherwise, why even have the water? I don't know what you think "thermal mass" means, but that isn't it.
I think I know what he was thinking, he thought that instead of moving the hot fluid from the hot side towards the cold side as is done in heat engines , you simply heat up the fluid/water and the heat travels down the fluid and reached the other end , sort of like when you heat a piece of metal at one end and after a while the other end heats up as well due to thermal conduction of the material.

Anyway @Prathyush this works for small distances only , but any efficient means of heat transfer especially over larger distances always involves moving the very medium/fluid itself instead of just relying on passive conduction.

That makes no sense. If relying on conductivity the water would have to be conductive. Otherwise, why even have the water? I don't know what you think "thermal mass" means, but that isn't it.
By thermal mass I meant something with very high specific heat capacity. Something that can store 1 terawatt day of energy.

I did not worry about conductivity issues, which was a mistake.

hutchphd
Homework Helper
I think turbines in the Gulf Stream might make more sense.

By thermal mass I meant something with very high specific heat capacity. Something that can story 1 terawatt day of energy.

I did not worry about conductivity issues, which was a mistake.
Well you should have worried about conductivity issues because just as I said in my previous post , passive heat conduction is only efficient in good thermal conductors , so then water is worse than metals so you would need not a pipe but rather a solid metal rod , but the other problem that I also said is that passive heat conduction is very inefficient over larger distance and is normally ever only used over small distance.
Like for example heat exchange ducts within a ventilation system or a heat sink radiator for electronics.

The moment you need to bring some thermal energy from place A to B which is even as far as a bedroom away you need a thermal fluid/agent which is a substance that absorbs the heat and is then physically carried from one place to the other. This is how air conditioning systems work for example. You have a fluid/gas and a pump that moves the fluid/gas.

In your case for your idea you would need lots of water pumps and lots of energy to pump that water

russ_watters
The moment you need to bring some thermal energy from place A to B which is even as far as a bedroom away you need a thermal fluid/agent which is a substance that absorbs the heat and is then physically carried from one place to the other. This is how air conditioning systems work for example. You have a fluid/gas and a pump that moves the fluid/gas.
Yes, that's basically it.

russ_watters
Mentor
By thermal mass I meant something with very high specific heat capacity. Something that can store 1 terawatt day of energy.
You are not trying to store heat, you are are trying to transfer it. Why do you think you need to store heat? What, exactly, does the water do?

I realize you've given up on your idea, but it would still be beneficial if you could fix whatever misunderstanding this is.

russ_watters
Mentor
I think I know what he was thinking, he thought that instead of moving the hot fluid from the hot side towards the cold side as is done in heat engines , you simply heat up the fluid/water and the heat travels down the fluid and reached the other end , sort of like when you heat a piece of metal at one end and after a while the other end heats up as well due to thermal conduction of the material.
If so, there's a jumble of unrelated concepts in there. Storage isn't transfer, Transfer through the metal isn't transfer through the water, etc.

I realize you've given up on your idea, but it would still be beneficial if you could fix whatever misunderstanding this is.
I understood the mistake I made, I said so in the 5th post of this discussion, I over estimated thermal conductivity by many orders of magnitude. Only when I sat down to calculate, I realized my mistake.
While writing this post I realized there is a fatal and unfixable flaw. I had overestimated heat flow capacity of metals by many orders of magnitude

Copper conductivity is 386 W/m/K. If we have to transport 1 terawatt heat over 10000Km, we would require material of unimaginable conductivity.