A Brief Note on Thermodynamics
by Danielle Fong
One of these days, I’ll try to write up the rules of thermodynamics so that people stop getting mislead. This is not a particularly well edited essay, but it should go up somewhere. Apparently there was a considerable armchair debate about what we are trying to do at LightSail on SciAm.com. Rebuttal below:
Ok, I’ll bite.
First of all if you’re actually looking for rebuttals, it’s usually easier if you post it to my email or some website I own (e.g. daniellefong.com) and have notifications for. We get an awful lot of media coverage and I don’t monitor everything.
Second, the efficiency we’re targeting is 70%. Not 91%. I don’t know where people got that from. We include all of the practical losses that people have mentioned — motor inefficiency (at our scale, typically 5% loss, not 10%, as some people seem to believe — it depends upon scale), friction, heat loss through our insulated tanks, etc. We are not actually there yet. If our first product is between 60% – 70% efficient we’ll be pleased, but we’re determined to push that as high as we can.
Third, it appears you are under some confusion about thermodynamics.
It is a slippery field, and I don’t blame you: both Bill Gates and his advisors made similar mistakes the first time through.
a) We’re not doing isentropic compression or expansion. The whole point of the water spray technique is to approximate an isothermal compression and expansion cycle — the water absorbs heat from the air rapidly. The correct first order approximation is that the heat capacity of the *mixture* is effectively added to the heat capacity of the air. Try deriving this from the 1st law, starting from T_water = T_air, and following the derivation of adiabatic compression without heat exchange to the outside that you see in any thermodynamics text.
Actual results have our output ∆T < 20 C and maximum hotspot ∆T = 60 C. Water spray actually cools. It is surprising how controversial this has been in the 21st century…
b) You’re using Carnot efficiency in an erroneous way. Compression and expansion are only part of the cycle. While it’s true using the generated heat alone in a heat cycle would grant you the efficiencies you describe, this is irrelevant, because we’re not doing that. There’s a whole other thermodynamic resource: *the compressed air* that this is wasting. So we’re not doing that.
Here’s an illustrative exercise.
A Carnot Cycle is perfectly reversible: run the cycle backwards, and 100% of the heat turns back into mechanical energy. How is this possible, one might ask, while at the same time being compatible with Carnot efficiency?
Several reasons: as a heat pump, the Carnot cycle turn W units of work into 1/(1 – Tc/Th) units of Th heat! There’s more heat, in joules, pumped than work put in.
This might seem to violate intuitions, but you can purchase heat pumps at any hardware store. You will notice that there are heat pumps and refrigerators with a coefficient of performance much greater than 1 widely available. This really works.
Now, draw a T-S diagram of a Carnot cycle for an ideal gas. It’s a rectangle in T-S space, the isothermal compression and expansion processes are horizontal lines, and the adiabatic processes are vertical.
Shrink the adiabatic processes to nothing, so that isothermal compression and isothermal expansion are at the same temperature. No heat is moved, and there is no net work. It is still a reversible Carnot cycle. But it doesn’t seem to do anything.
Why would you do a thermodynamic cycle if you get no net work energy out?
Answer: if you get energy out at a *better time*!
If you get 100% of the energy out that you put in, but at a different time, then this is an *IDEAL* energy storage cycle. You can’t get more efficient than that!
However, by your mathematics, you’ll have a 0% efficient heat engine.
The thermodynamic equations for a full heat cycle are *different* than for an energy storage cycle. You cannot just use them blindly. You have to go back to the first principles: the first and second law. (which, by the way, are never violated here — there is never entropy destruction in this or any other ideal reversible cycle).
All this said, this is an idealization. In fact there are losses in the process. Friction, for example. Resistance in our motor coils. Air turbulence running through valves. All this goes to heat.
What we do with this heat is that we collect it so that we expand air at as high a temperature as we can.
We don’t get as much energy out as if the energy never went to heat, but it is a small boost if we can get it. About 10% relative energy storage efficiency (E_out/E_in) for a 30 C heat increase if we’ve got it, nothing to sneeze at.
But even if we lose 100% of the extra heat, and have to expand at ambient temperature, our efficiency only goes down by that same 10% relative efficiency. It is not bad.
Also, it’s not so hard to insulate a large tank.
In general, while I applaud the efforts of people to work out things for themselves, you have to be extra careful that you’re not deluding yourself. It is worse to take a well known equation, misapply it, and declare impossibility, than it is to say that you heard about something but haven’t worked to complete understanding from the fundamentals yet.
It’s not actually working something from first principles if you get them wrong…
I appreciate your clarification, I saw the SciAm article and was curious where the commenters were going wrong. One note though; your link on this blog post isn’t directing to the article, while the twitter one works. For those looking for the proper link:
Where on earth do you get the time to actively blog and at the same time work on saving the world through lightsail?
it takes a reasonable amount of time to write; usually not too much, only a couple of hours. I have to write for my company anyway; sometimes I repurpose an internal communication.
So is it 60-70% efficiency in one direction you are hoping to achieve? It is not clear in your essay.
60 – 70% roundtrip.
I am Richard Li, an angel investor, PhD in Applied Physics from Stanford, current working on R&D at Invensense (8th fastest growing high tech company of North America in 2012 from Forbes).
I did following calculation:
Annual global electricity consumption is 2×10^16WH
1MWH requires a container equivalent to 1TBU.
Assuming solar and wind energy can supply 10% of total electrical energy consumed. Your solution could provide a storage for 10% of it. To supply the storage need of 1% of total electricity therefore requires: 2×10^8 BTU of containers.
There are 50,000 containership in the world with 5000BTU average capacity.
To store 1% of the total eletrical energy required, we need roughly all the containers in the world.
If each contained weighs 5 tons, to store 1% of the energy requires 1G tons of steel, an annual global production of steel…
Your calculation is correct, but you’re making an invalid assumption.
The main variation in electrical power is diurnal.
To buffer this, you need perhaps 6 – 12 hours worth of storage at a capacity rating of perhaps 50+% of peak usage will get you most of the required energy for running a largely (>> 50%) renewable powered grid.
Let’s be conservative and require 100% of the average power capacity, for 12 hours. This should pretty much power the whole planet.
2 x 10^16 W hrs * 12 hrs/(8760 hrs) = 27,397,260 MWh.
We’re trying to hit an energy density of about 1 container per MWh.
Ok. That’s a big number, but it’s about a ninth your value for the number of container ships in the world, and it’s a planet sized battery that should handle almost everything that you need.
A safe estimate for our containers is about 10 tons per MWh. So the whole thing should weigh about ~0.3 billion tons.
As a comparison, there are about 8 billion tons of coal consumed every year.
Also for comparison, the annual production of automobiles is about 80 million. At about 2 ton per car, that adds up to a planet sized battery in two years.
Larger scale storage will probably involve caverns, but there’s a good reason to distribute some amount of storage.
Thanks for the correction.
In your calculation, if we count for the energy efficient of 70%, the total tonnage of steel consumed is still on the order of 10^9.
To make 1 ton of steel, we have to consume 0.8 tons of coal.
This earth-wide battery will take a full year of global production of both steel and coal to make not including the steel and copper piping and wiring which should be on the same “earth-wide” order magnitude.
In theory, a concerted global Giant Leap Forward (where global population abstaining from sins including producing cars, buildings, transportation infrastructure as well as enduring cold weather without heating or hungry with less cooking) is possible (as has been carried out by former USSR or China under Mao).
In the real market economy, capital always flows to the places where marginal gain/marginal gain is the highest possible. The total energy produced by solar and wind is still a tiny percentage. So the market will not be activated until solar and wind are the best shot economically. This requires the lowest price among oil, coal and natural gas to go up tremendously.
However, we have seen how the world financial system and econmical system behave in 2008 when oil price went to $140/barrel ($105/barrel today, $20 in 2002).
For a more systematical and fundamental understanding of inevitability of the seemingly unexpected event of 2008, please read what King Hubbert wrote in 1980’s (www.hubbertpeak.com/hubbert/monetary.htm): the democratic system with the help of capitalistism (both of which we all thank for) propelled the exponential growth of montery system and population which is only stable with the material and energy growing exponentially with them. The peaking of energy/material (due to the finiteness of both) as he predicted in 1980 in early 2000, will lead to zero interest rate and/or hyper-inflation, both of which lead to the collapse of the financial system and together with the real economy.
2008 financial crisis, BP Gulf Deepwater Horizon Oil Spill (2010), Shell’s failure in drilling at Arctic (2013), all showed that the same symptom of peak oil reflected in different forms.
The technology helped us found more energy sources in the early phase and provides more efficient use of energy quantitatively but does not qualitatively resolve the finiteness of the earth and the infinity of exponential growth.
Please check this video out:
The objective is definitely to beat the market price or, in the worst case, the price of extraction and processing.
Would your technology improve the efficiency of split cycle gasoline or diesel engines. Split cycle engines dedicate some of the cylinders to air compression and the others to the combustion and expansion instead of having each cylinder do it all. It supposed to be quite a bit more efficient than regular engines and also allow for compressed air hybrids.
There’s a company near me that’s designing them. http://www.scuderigroup.com/technology/
Good call, it would help, yes :-) We have thought about it.
I think we need an affordable, efficient, and reliable energy storage solution in Ontario to reduce the amount of money we need to PAY other provinces and states to take our spare electricity from time to time. To have any chance of being affordable, the system should be of industrial size in order to optimize efficiency. Also, it should be located where reliable electricity is a must, such as at a hospital, as an alternative or complement to a conventional power plant. Software will probably also be an important component to determine precisely when to buy or sell power based on market and grid conditions. Because proximity to specific site (such as hospital) or at least population is necessary to minimize transmission loss, safety of the system is hugely important.
Best of luck with the project, I really hope that you can provide a good solution to storing renewables and balance the grid.
Also, wouldn’t this work even better as a solar thermal hybrid system? A solar concentrator could heat up the air about to enter the expander, allowing the whole system to return perhaps more energy than it took from the grid. The beauty is that you already have most of the system, only new cost is to add a solar concentrator either as a through on parallel segment or with heat-exchanger on the main line, and you end up with a solar thermal plant as well, generating clean power during the day, when demand is highest. The new solar plant would make use of the other components already paid for by the storage business (motor/generator, compressor/expander, tank, wiring, facility, software, maintenance, overhead…). Seems to me that’s the way to go, although it could mean you must retain ownership of the system and sell the service (electricity back up and electricity to the grid) instead of the device, because of the added complexity which could be too much for clients to deal with.
You probably understood that I meant trough, instead of through.
Numbers are the Supreme Court of science. However Godel proved that we may not prove everything. Science needs numbers. There must be Science and Physics Foibles!!
Thanks for your notes. I was wondering what is the difference (if any) between what LightSail and SustainX are doing.
We have a bunch of things we are keeping secret, because they moved from what they were doing to what we are public about a couple years ago. So we are different, and better, but I can’t tell you why ;-)