Steam powered rovers

Big_Al · 2018-11-08 08:22:12

This may seem to be crazy but it’s really not. The lower gravity allows for heavier vehicles and a wider selection. Dirty water could also be put through it to help clean it. This is a unconventional approach but it may help set up a rail system too.

JoshNH4H · 2018-11-08 10:22:24

Hey Big_Al,

I'm assuming you're talking about rovers build on Mars rather than sent from Earth, since for things sent from Earth mass really does matter.

A steam engine as we normally think about it is basically two things: A coal furnace hitched to a piston heat engine with water/steam as the working fluid.

Coal is wholly inappropriate for Mars, because there's no Oxygen atmosphere and no coal.

I would argue that a steam engine, as we normally think of it, is inappropriate too. The main reason is their extreme inefficiency. Power plants these days use steam turbines instead because they're way more efficient at extracting energy.

If we're looking to use chemical fuels on Mars, I think the right solution is either an internal combustion engine (for low power) fueled by an alcohol and compressed Oxygen or a gas turbine (for higher power) also probably fueled by an alcohol and compressed Oxygen. For lower powers I think you'd probably want battery-electric.

A steam turbine might make sense for a Concentrated Solar Power system, though.

Big_Al · 2018-11-08 10:32:31

Good point I like your idea better.

louis · 2018-11-08 14:45:52

Another possibility is harnessing temperature change to use frozen CO2 as a power source...

Here's a link explaining how it works:

https://newatlas.com/carbon-dioxide-eng … ars/36443/

kbd512 · 2018-11-08 19:31:11

Using CO2 expansion would be a lot more viable source of motive power than steam, as a function of achievable power-to-weight ratios. Small vehicles such as motorcycles could easily use CO2 cylinders (Scuba tanks) to power piston engines, for example.

Like so:

Aussie Motorbike that runs on thin-air!

SpaceNut · 2018-11-08 21:49:41

Thanks for the running on air bike here is some more of it with numbers...

Air-Powered Motorcycle Runs on Scuba Tank, Rotary Engine

Yamaha WR250R frame, and added a scuba-diving tank and a 25-pound engine to power the rear wheel. Squeeze the throttle and air is released to accelerate the bike. And its stats are impressive. The O2 Pursuit gets 62 miles of travel on a full tank, and can hit a top speed of 87 mph.

The Air-Powered Motorcycle by Jem Stansfield

Top speed is 18 mph (29 kph), range is 7 miles (11.2 kilometers) between compressed air fill ups.

This Bamboo Scooter Runs On Nothing But Air

Australian Students' Air-Powered Bike

ComputerGeneratedMotorcycle.jpg.aspx?width=460

The engine is powered by two tanks of compressed air, and with them the engine hits 3,000 rpm almost instantaneously. This obviates the need for a gearbox, so there is none. With only a single gear, the bike has only one lever on the handlebar: the brake.

kbd512 · 2018-11-08 22:04:15

SpaceNut,

I wonder if we could get substantially more range using the more efficient expansion cycle of the new Libralato rotary engine. There'd certainly be less seal wear through less metal-on-metal. I'm sure we could make that thing lighter for use on Mars and install a pressure regulator to limit top speed to something slightly less likely to kill the rider in an accident.

Edit: On second thought, that rotary piston engine already appears to be very efficient.

Last edited by kbd512 (2018-11-08 22:07:02)

JoshNH4H · 2018-11-09 17:43:14

Hey louis,

Interesting article! If I recall correctly there was a thread about that a while back but I don't think I got involved in that one.

While dry ice definitely has potential as an energy store, I don't think that particular device is the best way to extract energy from it. The key fact about the leidenfrost effect that it's based on is that it slows down heat transfer, after all, which is the opposite of what you'd want. More of a curiosity than a useful technology in my opinion.

Having said that, it's been pointed out various times on this forum that low nighttime temperatures on Mars mean that it's relatively easy to freeze CO2 out from the atmosphere. For reference, solid CO2 has a density of 1.56 g/cc and liquid CO2 has a density of 1.1 g/cc.

Because it liquefies at a relatively low pressure and high temperature, CO2 happens to be a poor choice of gas for compressed gas applications without an external heating source. Virtually any other gas is better. On Mars, Nitrogen is probably the appropriate choice.

Having said that, I'm interested in the possibility of using liquid CO2 with a source of heat from the ambient environment as an energy store. To start, here's some numbers:

The heat of vaporization of liquid CO2 is 15.326 kJ/mol. The specific heat capacity of CO2 at constant volume is 47 J/mol-K. The triple point is at -56.6 C (216.6 K) and 510 kPa.

Let's say you store your CO2 as a liquid near the triple point, -57 C. The pressure will be 5 atmospheres, 500 kPa and once released you further heat the gas to -20 C. Let's say that through a turbine or piston you reduce the pressure and allow the gas to cool to a temperature of 198 K, when it will begin to freeze. The outlet pressure will be 1.9 atm, at which point you can reheat the gas to -20 C and re-expand (reducing the pressure once again by 62%) if you so choose. The benefit is a more efficient use of LCO2. The cost is that you'll get a worse efficiency, because you need to heat your CO2 by a larger amount.

The heat input required for the first stage once the CO2 has boiled is roughly 1300 J/mol (30 kJ/kg), and you will generate up to about 675 J/mol (15 kJ/kg), depending on your efficiency. The reason your efficiency is so good on such a small temperature differential (the theoretical efficiency here is 52%; carnot efficiency between -20 C and -75 C is just 22%) is that it's possible to obtain the energy of vaporization from the environment which, while cold, is not that cold, usually. You might use methanol in a heat exchanger to transfer the heat from the ground to the generator.

As far as the question of where that heat is supposed to come from, I believe there's actually a pretty simple answer: From freezing water which, as we all know, freezes at 0 C and releases 334 kJ/kg in that transition.

This is not a good fuel source for a vehicle, but actually seems quite promising for stationary applications. A good nighttime energy source for a colony if you can freeze the CO2 during the day, perhaps?

Edit: I wrote this post over several days and I see that there's been substantially more discussion in the meantime

SpaceNut · 2018-11-09 18:16:21

Yes Running on compressed air

The heat source could be pebble reactor, rtg or even a kilowatt reactor as we are not just looking for the heat source but also some electrical to make things all work together.

JoshNH4H · 2018-11-09 18:26:34

I don't think you would want to use this kind of system with a nuclear reactor because a gas or steam turbine would be much more efficient. The main benefit to this system imo is that you can use a very low-grade heat source

kbd512 · 2018-11-09 19:15:02

Josh,

Is there any reason why a Pu238 heat source wouldn't work?

JoshNH4H · 2018-11-09 21:09:00

kbd512,

No reason whatsoever from a technical standpoint. The only reason is that, in my judgment, there are better ways to convert the heat from the Pu-238 into usable energy.

From my perspective the biggest benefit to the system I described is that it can operate with an extremely low-grade energy source. If I recall correctly, RTG sources generally operate at temperatures of several hundred degrees centigrade, meaning they're way overmatched for a system that can operate happily with a hot-side temperature of 0 C.

The other thing is that, from my perspective, the best thing about RTG is that it will produce power at a predictable, consistent rate with no fuel consumption for decades. On the other hand this system consumes liquid CO2 as a sort of "propellant" so I think the benefits of the two systems are mismatched.

Based on the power production of an RTG unit (usually in the range of 1 kWt, if I recall correctly?) I think you'd want to look more towards a piston or turbine system operating at higher temperature, probably with Nitrogen, Helium, or Argon as a working fluid. I know there's been some advances in microturbines lately but a piston system is simpler, if a little less efficient.

So: It would work but it's not the best use of the system imo.

kbd512 · 2018-11-10 16:21:35

Josh,

I was thinking of something more along the lines of a RHU inserted into an insulated pipe that heats the CO2 to increase the rate of expansion.

RTG's essentially contain several larger Pu238 pellets, as would be found in RHU's, that are inserted into graphite blocks. The thermal output of a MMRTG is overkill for a motorcycle or air tool application. The 250Wt GPHS (General Purpose Heat Source; 9.948 cm wide x 9.32 cm deep x 5.82 cm high) blocks in (RTG's) and 1Wt RHU (Radioisotope Heater Unit) tubes both contain capsule shaped Pu238 pellets clad in graphite heat spreaders. The geometry of the Pu238 pellet and graphite heat spreader tube or block determines how many watts of heat are spread over a given surface area for a particular application.

In this proposed application, the RHU tube is located inside the insulated gas line between the LCO2 tank and the air engine. The heated CO2 increases gas volume, thus pressure in a fixed geometry gas line, to drive the engine at greater efficiency per mass unit of gas expelled.

The Australian design already achieves a 60+ mile range using a 300 bar scuba tank and no additional thermal energy imparted to the expanding air driving its rotary piston engine. The addition of the RHU should prevent the expanding CO2 from freezing in the feed line and increase the overall thermal efficiency of the engine by imparting more kinetic energy to the expanding gas without additional losses incurred from incorporating a separate system that requires additional input power to heat the gas. The real question is how much thermal power is required and can a reasonably sized RHU provide that power.

My intent was to incorporate a nuclear-enabled thermal power system component that permits the use of prime movers only reliant upon gas kinetic energy to limit the need for shielded and radiation hardened electronic components. All batteries in practical electric vehicle applications use micro-electronics to regulate individual cell voltages during charge and discharge. There's nothing wrong with that, but the controller must be rad-hard and rad-hard microprocessors are every penny as expensive as small chunks of Pu238 as a function of the materials required, special fabrication methods, and low production volumes. Maybe this will change in the future, but the chips are easily a quarter million to a million or more per copy and the other specialized electronic components on the board are also substantially more expensive than their commercial or industrial cousins.

We've already discussed at great length why internal combustion engines are impractical for vehicle use on Mars and we've also discussed how the mass of suitable batteries could quickly become unmanageable (since batteries in aerospace applications are completely unlike the batteries that consumers plug into their cordless drill). It's hard to argue that CO2 powered vehicles and tools would be a much simpler and more physically robust system in the harsh Martian surface environment that requires far less technology to implement. Air powered tools and vehicles obviously do require suitable infrastructure, namely a CO2 compressor with an electrically-driven vacuum pump fed by a properly regulated electrical power supply, but we already require that technology for propellant production to obtain rocket fuel and I see the use of air tools and vehicles as a synergistic system using already-required infrastructure for that purpose.

Anyway, I welcome any thoughts on this. I'm sure there are plenty of potential problems I haven't considered.

JoshNH4H · 2018-11-10 18:02:33

So the idea is, in effect, to use the RHUs to heat up the CO2 (instead of liquid water as I have proposed) and thus extract more energy out per unit volume of fuel.

So far I'd say we're starting from a solid place. In fact, the reason I suggested multiple stages of heating/turbines is that heating to -20 C is suboptimal for extracting all that pressure-energy--Heating to -20 C and then allowing it to cool by expansion to 198 K still leaves a residual pressure of almost 2 atmospheres.

Let's say the inlet pressure remains at 500 kPa and you want the outlet pressure to be 10 kPa (10 times Martian ambient). The pressure change across that differential would be to decrease temperature by a factor of 2.75 (I have been assuming ideal gas behavior in this thread which makes my numbers somewhat inaccurate. Consider them to be estimates). That means that your ideal "hot" temperature for the gas would be 275 C. This is a nice operating temperature, actually, because it's right near the upper limit of common steel materials.

Of course there's no particular reason to use the critical pressure. The critical temperature is somewhat below average Martian ambient conditions, and actually because of the narrow liquid range near the critical point you might want to be at a somewhat higher temperature/pressure.

Speaking roughly, the amount of energy you can get per unit of LCO2 is proportional to that temperature change (not exactly because of changes in heat capacity and Cp/Cv with temperature but close enough). Using this temperature differential (350 C instead of 55 C in my design) you'll get roughly 95 kJ of work per kg of LCO2 and the "efficiency" will be the same 52%.

Obviously the same caveat about efficiency applies, namely that this is not a true measurement of efficiency because it disregards the energy used to liquefy and pressurize the CO2.

One number that's relevant here is the energy cost of freezing CO2 out of the atmosphere. The heat of sublimation of CO2 is 571 kJ/kg. Let's say your cold side is at a temperature of 190 K (somewhat below the sublimation temperature) and your hot side at 250 K (a bit warmer than the martian ambient). Refrigeration is cool because you can pump more heat than the amount of work you put in. The carnot coefficient of performance between these two temperatures will be 4, meaning it will cost you 140 kJ/kg of CO2 to freeze out of the atmosphere.

Of those 571 kJ, about 200 kJ will be retained to melt and pressurize the CO2 into a liquid. This can actually be much more efficient because you're pumping from a cold side of (say) 190 K to a hot side of (say) 230 K for a COP closer to 6.

There was one thing you said that isn't correct:

kbd512 wrote:

The heated CO2 increases gas volume, thus pressure in a fixed geometry gas line, to drive the engine at greater efficiency per mass unit of gas expelled.

Heating gas in a line doesn't increase the pressure unless the line is closed at both ends: Instead, the pressure remains roughly constant, the temperature rises, and the gas moves more quickly through the line. As far as thermodynamic engines go I think this is a better thing anyway.

kbd512 · 2018-11-10 20:18:37

Josh,

Thanks for the food for thought. I must profess ignorance about this. I've just started reading about how this could work by going through some documents I have on CO2 heat pumps that contain the equations used to determine the thermodynamic behavior of the system. You clearly know a lot more about this than I do.

And yes, that statement was very poorly conceived. In a gas turbine (air tool) where the exhaust expulsion process is continuous, my statement would be false. However, I was thinking of a cyclic piston engine (the kind that was actually tested in the O2 Pursuit air powered motorcycle), where there is a period of time when the intake port is briefly cut off from the supply of gas (trapping the gas in the tube and increasing the pressure before being fed into the pump; perhaps too brief to be of any real consequence). It was just a half-baked idea about a the RHU tube with a de-facto valve (the pump's intake port) that briefly holds gas in the tube and then expels it into the pump as the piston(s) rotate. I've no clue how useful that would be or if the pressure increase is negligible.

Just to be clear, my only intended uses for this technology were air tools for construction around the Mars base and very light vehicles for base transportation. If we must already store LCO2 for the manufacture of LCH4, then this is just another use case for it. I fully realize that lights and other electronics require more suitable energy sources, like batteries, provide power. If, however, we can devise simplistic mechanical systems that don't mandate the same level of environmental-hardening as electrically operated tools, that would be beneficial.

My conceptualized use case is that I have an astronaut who must erect a habitable structure a couple of kilometers away from the BFS. He or she hops on their CO2 powered motorcycle, quickly traverses the short distance to the worksite without undue effort, reaches into a bag of tools, pulls out an air-powered drill, hooks a short hose from the nuclear unit attached to the motorcycle to the tool, drills the holes for cable stays to anchor the radiation shielding support members in place around the habitat module, puts the tools away after a couple of hours of work, drives back to the BFS, refills the tank, and then the next astronaut repeats that process until the surface habitat construction is complete. Heavy construction equipment like a small tracked vehicle that grades the surface the habitat was erected on would be battery powered. A small crane used for hoisting the support members over the top of the habitat to support the weight of radiation shielding powdered regolith bags would use a combination of electrical power for the vehicle and pneumatic or hydraulic power for the crane. Anyway, that's the kind of stuff I had in mind.

I know that high duty cycle tools in automotive or airframe shops and on construction sites tend to be pneumatic and jobber type tools tend to be battery powered or corded. It's really dependent upon the specific application and environment where the tool is used. On Mars, there's a problem getting rid of the waste heat that an electric motor generates. A 1kWe electric motor that's 95% efficient still has to get rid of 50Wt. In practice, small electrical power tool motors are rarely that efficient. The atmosphere is super thin, so the battery powered tools will not be as powerful as the air tools or incur the added complication and weight to adequately cool the motor. The atmosphere is of little use in that regard, despite being much colder than Earth. In turn, the cold is very problematic for the batteries without insulation, which then require more complication associated with thermal regulation for high current drain. Solvable? Sure. Easily? Probably not. The pneumatic tools largely bypass those problems by continuously carrying away heat from operation with the gas that's driving the tool. I suppose a gas cooled electric motor would also work, but then you need the coolant CO2 and battery to operate the tool. At that point, why not just use an air tool?

SpaceNut · 2018-11-10 21:34:30

The description is more like a desiel engine with a glow plug for operation with the value train or injectors feeding in the fuel into the chamber before heating it making it expand after its compressed it then would open on the up stroke to push the spent fuel out.
So the question is how fast can we heat the co2 and how fast can we cool it for reuse....

JoshNH4H · 2018-11-11 15:48:32

Hey kbd512,

My high-level take is that this is a good idea with a lot going for it. A jar of LCO2 is pretty lightweight, easy to use, safe, reliable, and fairly easy to transport. Assuming you get 80 kJ/kg out of the LCO2 when all is said and done (pistons and turbines being less than perfectly efficient, after all) you're storing about 0.025 kWh/L. The tank itself might be a pain to lug around to where you need it but the mass delivered to Mars can be quite small.

For reference, the pressure range we're discussing is similar to what you would see in a propane tank. If you're using a spherical tank make from Aluminium 7075 and a safety factor of 5 (standard for pressure vessels) and a design pressure of 10 atm you're looking at a mass (just for the tank) of 250 kg/m3 of internal volume.

In The Case for Mars Zubrin suggested that we could run things off MethLOX siphoned off from the fuel generated by the Sabatier reaction, burned in an internal combustion engine. Incidentally, as has been mentioned previously, you'll still want to dilute the MethLox with some CO2 to keep it from burning too hot.

CO2 has a higher heat capacity than Nitrogen. Based on the NIST WebBook, the heat capacity for N2 at 1000 K is 32.5 J/mol-K and for CO2 is 54.5 J/mol-K. This means that the appropriate mole ratio of CO2 to O2 is 2.24, compared to 3.76 of N2:O2 in Earth's atmosphere.

The stoichiometric mass ratio of CH4:O2 is 1:4, so this implies that the mass ratio of (CH4 and O2) to LCO2 will be 5:1. The mass ratio of LCO2 to LCH4 will be 25:1 and of LCO2 to LOX will be 6:1.

What this makes me wonder is what the solubilities of each of these in LCO2 is. It's something that probably hasn't been well-studied, but there's huge gains to be made from storing LOX or LCH4 (Which are substantially colder than the Martian ambient) vs. LCO2 (which is liquid at mild pressure under Martian ambient) and if you can solvate the fuel and oxidizer in LCO2 there would be big gains to be made.

I know very little about modern batteries or rad-hardening of electronics. Fuel cells seem to be a potentially viable alternative, I know NASA has used them in space in various contexts in the past. I would say that if it improves mission operations even a little bit it's worth spending a few million dollars to rad-harden some batteries.

JoshNH4H · 2018-11-11 20:03:11

kbd512 mentioned that his knowledge of thermodynamics is not strong. Mine also is not strong: Thermodynamics is a notoriously difficult subject and most of what I know is what to ignore when analyzing a thermodynamic engine. Luckily, that is the relevant portion for most practical applications. I don't know how much kbd specifically knows or doesn't know, but in this post I would like to cover the basics of thermodynamic engines for anyone who cares to learn.

My background is in mechanical engineering and my knowledge of the subject comes from a single class, which in my opinion was poorly taught by a professor who was an expert in his field but didn't care for teaching. Thermodynamics is in some ways the bastard child of physics and chemistry, relevant to both but firmly part of neither.

Anyway, I'm going to start by defining the relevant variables:

T: Temperature, a familiar measurement which should be measured on an absolute scale (i.e. Kelvin or Rankine)
S: Entropy, measured in J/mol-K or J/kg-K. I'll be honest: I don't know what entropy is and I'm not sure anyone does. It has something to do with "disorder" in a system. Hotter things have more entropy than colder ones, all else equal; gases have more of it than liquids, which have more of it than solids. Entropy after a process will always be the same or higher than before it.
H: Enthalpy or heat, measured in J, J/kg, or J/mol. This is a measurement of heat added to or subtracted from the system to get it to a certain state, which usually means some amount of fluid.
Q: This is a measurement of heat being added to or subtracted from a system.
U: Internal Energy, measured in J, J/kg, or J/mol. This is a measurement of the energy stored in atomic vibration and physical or chemical bonds.
W: Work, measured in J, J/kg, or J/mol. This is a measure of the useful (usually mechanical) output of a thermodynamic process.
X (technically the greek letter chi): Quality. This refers to the portion of a fluid, by mass, that is vapor. For example, you might have a X of 0.7, meaning that 70% of your fluid is gas and 30% is a liquid. Turbines will not work with a quality factor below roughly 0.9. Pistons are somewhat more robust but you will have difficulty clearing the piston on a downstroke if there's too much liquid in it.

The first law of thermodynamics is:

dU=dQ-dW

"d" as used here refers to an infinitesimal change. You can replace the "d" with a "∆" (change in) without changing your understanding of the First Law. This equation means that the change in the internal energy of a system (the energy stored in molecular vibrations and chemical bonds) is equal to the amount of heat added to the system minus the amount of work done by the system.

In a thermodynamic engine like a piston, a rocket engine, or a turbine we are converting heat energy into useful work by exploiting a temperature differential. Below, I have included a Temperature-Entropy diagram for a typical one-stage steam turbine.

images?q=tbn:ANd9GcRF203xLKkyqc-cg0LPeFVVlSPBkF8vhgJE4zgJHVMAmrAupuT1

Entropy is on the horizontal axis and Temperature on the vertical axis. To the left of the red curve water is entirely in the liquid state. To the right of the red curve water is entirely in the gaseous state, as steam. Under the curve water is partially vaporized, with a quality between 0 and 1. Here's what's going on in that graph:

Between points 1 and 2, water near its boiling temperature is compressed (i.e. there is an input of work)
Between points 2 and 4, the water is heated to its boiling point at said pressure (at point 3) and then further heated until all of the water has vaporized, and then further heated beyond that temperature (i.e. there is an input of heat energy)
Between points 4 and 5, work is extracted from the fluid using a turbine. In the idealized model this is adiabatic (Q=0) and isentropic (∆S=0). A process that is isentropic is also reversible because no energy has been lost. Real-world turbines can achieve roughly 85% of the work output of the isentropic value.
Between points 5 and 1 the fluid is cooled back to its original state.

The value that we as users are interested in is the efficiency. Here's how you calculate it:

Efficiency is the net work produced by the engine divided by the heat input to the engine.

The net work is the work output (between points 4 and 5) minus the work input (between points 1 and 2).

In the abstract, work done by a compressor is:

dW=d(PV)

In general, this is difficult to solve analytically because you need to determine how pressure affects temperature and vice versa when temperature is not constant (PV=nRT is not useful here). However, water is much easier because the volume doesn't change with pressure. Therefore, we have:

W=V∆P

To calculate the work output, we use the difference in H between points 4 and 5. For water, we can look this up in Steam Tables and look at the difference in H between points 4 and 5.

Calculating the heat input is quite simple: It's equal to the difference in H between point 4 and point 2.

If working with Carbon Dioxide, the process is quite similar. I just discovered that the back of my old Thermo textbook has steam tables for CO2, meaning I can give more accurate numbers for efficiency and work output. I will do this in a following post.

SpaceNut · 2018-11-11 20:43:20

Entropy seems to be heat capacity which is related to the materials coefficent of how heat is transfered through it. Heat capacity, ratio of heat absorbed by a material to the temperature change. It is usually expressed as calories per degree in terms of the actual amount of material being considered, most commonly a mole (the molecular weight in grams).

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. In physics, thermal conductivity (often denoted k, λ, or κ) is the property of a material to conduct heat. It is evaluated primarily in terms of Fourier's Law for heat conduction. Heat transfer occurs at a lower rate across materials of low thermal conductivity than across materials of high thermal conductivity.

Thermal conductivity is a property of a material that determines the rate at which it can transfer heat. Each material's thermal conductivity is determined by a constant, λ, calculated as: λ = (Q x L) / (A x t x Δ T) where Q is heat, L is the thickness of the surface, A is the surface area, t is time, and ΔT is the difference in temperature.

JoshNH4H · 2018-11-11 21:18:35

Hey SpaceNut,

SpaceNut wrote:

Entropy seems to be heat capacity which is related to the materials coefficient of how heat is transferred through it.

With all due respect this is not even close to right.

While I cannot confidently say what entropy is, I can very confidently say that it is not the same thing as the heat capacity. The heat capacity measures the amount of energy it takes to raise the temperature of a material. Entropy is something different, measuring the state of that material.

The coefficient of heat transfer has to do with how well a material conducts heat and it is not related to the other two.

IanM · 2018-11-11 21:21:51

From what I understand, entropy is essentially the number of states a system can be in at any given time (or the natural log thereof, IDK), but more intuitively it's the amount of energy that can't be used, which never decreases over time. I could be wrong, though.

JoshNH4H · 2018-11-11 22:07:17

IanM wrote:

From what I understand, entropy is essentially the number of states a system can be in at any given time (or the natural log thereof, IDK), but more intuitively it's the amount of energy that can't be used, which never decreases over time. I could be wrong, though.

From what I've read it's something like that, but if you think about it there's a lot of operational problems with this definition. Here's two: How in the world are you supposed to count these states when there's an infinite number of them? And how do you end up with J/mol-K as the unit describing a number?

SpaceNut · 2018-11-11 22:10:38

time cancels out of each part.... since each state is a measurement in time...

IanM · 2018-11-11 22:22:53

According to Wikipedia (https://en.wikipedia.org/wiki/Entropy), it's essentially the number of states in a given system that are consistent with the given parameters (pressure, temperature, etc.), which I think are finite but really hard to count. Apparently it's the natural log of that multiplied by the Boltzmann Constant, which has J/K units, hence entropy has J/K units (while entropy/mole is J/molK).

SpaceNut · 2018-11-11 22:47:47

A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. Here α has the dimension of an inverse temperature and can be expressed e.g. in 1/K or K.

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