Heat Engines, Entropy and Counter-Intuitiveness

[albroun]

I am not a physicist and have no mathematical understanding, but I am very interested in the fact that heat engines need a cold sink, simply by virtue of the Second Law of Thermodynamics. As I understand it, as the temperature of the cold sink rises, its entropy increases at a faster rate than the rate at which the entropy of the hot source declines as its (the hot source's) temperature falls. It is only by virtue of this that a heat engine can work. The cold sink can be the environment. Therefore if a heat engine relying on its surroundings as its cold sink is in an environment as hot as itself it won't work! Likewise a power station needs cooling towers and a steam engine needs a condenser.

I had previously thought that heat engines worked by heat being some kind of substance exerting a force, but this I now understand to be incorrect. Yet that would seem to be a more intuitive way of looking at things. But heat engines don't seem to work in this intuitive kind of way. Certainly I find myself mystified by the need for the cold sink. I had always wondered why a steam engine did not simply keep recycling the heat from its steam instead of ejecting it.

But what is so fundamentally counter-intuitive about this to me is that it is as if the universe is like some kind of devilish accountant who always has to ensure that there is never any profit! Infact, not only is there never any profit; there is always a loss.

Has anyone ever contemplated this mystery? Or is this just a consequence of some fundamental misunderstanding I have about thermodynamics? If so please correct me (without maths as I cannot get my head around equations).

Many thanks.

 

[Drakkith]

Put simply, that's just the way it is.

Your standard heat engine works by heating up something, like steam or air, and using the pressure provided by the expansion of the gas to provide force for moving the engine and everything else. Since heat is simply kinetic energy, the molecules in the air acquire more speed when heated and exert more of a force on the engine. Now, since we can't transfer heat from something colder to something hotter without doing work, the air in the engine must be cooled or else nothing will happen. Hence the need to have a cold sink to transfer heat to.

I'm not sure about the whole entropy thing, but I don't believe it in itself is the cause of working heat engines. Entropy is just a measure of disorder and whatnot of a system. It isn't a physical substance any more than heat is.

 

[russ_watters]

Consider a hydroelectric dam. The turbines absorb a lot of the energy stored in the dam, but they don't absorb all of it. There still has to be some flow and pressure left to carry the water away from the turbine! See, the dam and turbine just interrupts the natural flow flow of the river, but the flow still has to be there to satisfy the laws of thermodynamics (and avoid flooding over the top of the dam!). The same goes for any heat engine. Light a fire and heat flows from hot to cold. The steam engine turbine can't absorb all of this heat because it can't convert 100% of its input heat into mechanical work, so there is some residual heat left that must still be allowed to flow to the cold reservoir otherwise it will "overflow" the boiler (kaboom!).

 

[albroun]

Thank you for the clarification. There seems however to be still something counter-intuitive going on here. It seems as if the hot source has to "know" in advance that there is a cold sink to dump waste heat into in order to flow in that direction, especially bearing in mind that (at least in various diagrams I have seen) the cold sink is used AFTER the work-generating part of the system.

This kind of phenomenon seems to suggest that we are dealing with a system functioning as a whole, rather than simple temporal linear causality. Again, I have probably misunderstood a crucial point, but this notion of a whole system (in which past, present and future co-exist simultaneously) might also be a way of looking at the double split experiment in quantum physics.

To return to my devilish accountant, it is as if for anything in the universe to function, the sums have to be added up first. If the accountant declares that the books have been balanced in the correct way, then the process can take place, but cannot if the sums do not work out. The universe appears to be a mathematical system rather than a "physical" system, which makes me think of the simulated reality hypothesis. When I started reading about thermodynamics this struck me very strongly. But again this might just be my lack of understanding of the core concepts.

 

[Curl]

The reason you have to eject heat is because it comes out at a lower temperature than the input. You cannot move thermal energy from low temperature to high temperature; it will never happen.

And why are you so depressed about the "devilish accountant who always has to ensure that there is never any profit!" ? That is not true, there is gain all the time (sun is out today, we are collecting energy).

 

[albroun]

Well I am not depressed about it. Just fascinated and curious.

 

[russ_watters]

Thank you for the clarification. There seems however to be still something counter-intuitive going on here. It seems as if the hot source has to "know" in advance that there is a cold sink to dump waste heat into in order to flow in that direction, especially bearing in mind that (at least in various diagrams I have seen) the cold sink is used AFTER the work-generating part of the system.

Not really, no. The heat in a steam engine is forced by a pump to flow from the boiler to the turbines and from the turbines to the condenser. It doesn't have to know where it is going to end up.

 

[Drakkith]

Thank you for the clarification. There seems however to be still something counter-intuitive going on here. It seems as if the hot source has to "know" in advance that there is a cold sink to dump waste heat into in order to flow in that direction, especially bearing in mind that (at least in various diagrams I have seen) the cold sink is used AFTER the work-generating part of the system.

This kind of phenomenon seems to suggest that we are dealing with a system functioning as a whole, rather than simple temporal linear causality. Again, I have probably misunderstood a crucial point, but this notion of a whole system (in which past, present and future co-exist simultaneously) might also be a way of looking at the double split experiment in quantum physics.

To return to my devilish accountant, it is as if for anything in the universe to function, the sums have to be added up first. If the accountant declares that the books have been balanced in the correct way, then the process can take place, but cannot if the sums do not work out. The universe appears to be a mathematical system rather than a "physical" system, which makes me think of the simulated reality hypothesis. When I started reading about thermodynamics this struck me very strongly. But again this might just be my lack of understanding of the core concepts.

Think about it this way. Say we have a sterling engine with two pistons, one for the hot side, one for the cold side. When you first apply heat to the hot side, the gas inside the piston is at the same temperature as the piston, all of which is cooler than the heat source. As the gas expands it forces the piston to move and on the return stroke the hot air is moved to the cool side.

Now, imagine there were no cool side. What would happen? The hot air would get to the other side, but there would be nowhere for the heat to go for the air to cool down. So when the air gets pushed back into the hot side again, it is still hot and cannot be compressed as well as cooler air. This results in the engine simply stopping after only a few strokes of the pistons.

There was no need there for the hot side to "know" about a cold side at all. The engine and gas inside were initially cooler than the heat source, so the engine produced work until it reached equilibrium with the heat source. Having a cool side simply allows the heat to be removed from the engine.

 

[olivermsun]

Your system did "know" about the cold side, though -- the original gas in the piston started out colder than the hot side and that's why it expanded when it was exposed to the hot side.

 

[albroun]

Not really, no. The heat in a steam engine is forced by a pump to flow from the boiler to the turbines and from the turbines to the condenser. It doesn't have to know where it is going to end up.

But if instead of a condenser there was a furnace, it would never get there??

 

[Drakkith]

Your system did "know" about the cold side, though -- the original gas in the piston started out colder than the hot side and that's why it expanded when it was exposed to the hot side.

There wasn't a cold side. The engine was simply at a lower temperature.

 

[russ_watters]

But if instead of a condenser there was a furnace, it would never get there??

Pumps make fluids flow by increasing the pressure. So yes, you can make the steam flow around and around in the loop even if you replaced the condenser with another boiler. But because you removed the path for heat rejection, you'd lose your output work even before the bomb exploded.

 

[albroun]

Pumps make fluids flow by increasing the pressure. So yes, you can make the steam flow around and around in the loop even if you replaced the condenser with another boiler. But because you removed the path for heat rejection, you'd lose your output work even before the bomb exploded.

The pump requires an energy source itself so presumably it would not generate work. However, supposing there is no pump within the engine, and it is purely using the pressure generated by the steam to move the piston, and AFTER the pressure the steam generates instead of being cooled it is SUBSEQUENTLY not allowed to be cooled ... then presumably according to the laws of thermodynamics the piston would not have moved in the first place! (backward causation?)

Unfortunately things are not helped by the fact that not only do I have no background in physics or maths, but also none in engineering so I have very little idea as to exactly how steam engines work.

 

[russ_watters]

The pump requires an energy source itself so presumably it would not generate work.

Yes: remove the condenser and your pumping energy becomes bigger than the output of the turbine (before the boom).

However, supposing there is no pump within the engine, and it is purely using the pressure generated by the steam to move the piston...

Boilers do not generate a pressure difference to move steam in a heat engine - they are just coiled-up pipes. If there's no pump, the entire system will be at the same pressure everywhere and there will be no flow.

 

[olivermsun]

There wasn't a cold side. The engine was simply at a lower temperature.

Even in your one-cycle Stirling, there has to be a store of air held at a cold temperature, separate from the "hot reservoir," for there to be anything to expand in the first place. No heat differential = no expansion. That's the point I'm making in relation to the OP's questions.

 

[Drakkith]

Even in your one-cycle Stirling, there has to be a store of air held at a cold temperature, separate from the "hot reservoir," for there to be anything to expand in the first place. No heat differential = no expansion. That's the point I'm making in relation to the OP's questions.

Sure. But that isn't a cold side. That's the point I was trying to make. The heat doesn't "know" anything.

 

[olivermsun]

The heat knows that the air in the piston is colder than it is, right?

 

[Drakkith]

The heat knows that the air in the piston is colder than it is, right?

No, the heat isn't a "thing". It is a measure of the average kinetic energy of the particles that make up a material. If something is colder than something else, its particles are moving and vibrating and such at a slower rate.

 

[SpectraCat]

No, the heat isn't a "thing". It is a measure of the average kinetic energy of the particles that make up a material. If something is colder than something else, its particles are moving and vibrating and such at a slower rate.

Whoops .. you are confusing heat and temperature I think. Temperature is a measure of average kinetic energy .. heat is the flow of thermal energy, i.e. heat is always a measure of the change in thermal energy.

Statistical mechanics is probably the best way to understand why the heat doesn't have to "know" where the cold side is in order to flow. Random collisions transfer energy between the molecules, or atoms, or lattice vibrations, or whatever other characteristics of the system can store energy. In an individual collision, energy can be transferred in either direction (i.e. it can flow from the thing with higher energy to the thing with lower energy, or the opposite), however the probability is higher that it will flow from higher energy to lower energy. This is simply because there are more possible configurations where the energy is distributed over both things, than where it is concentrated in one thing .. this is essentially the microscopic definition of entropy. Thus if we sum up the effects of many such collisions, we find that the net result is that the energy tends to flow from things with higher energy to things with lower energy.

If two ensembles of such things (i.e. molecules, atoms, lattice vibrations, etc.) with different distributions of internal energies (i.e. temperatures) are brought into contact, then the net effect of the collisions over time will be a net transfer of energy between the two populations until they both have the same distribution of internal energies .. i.e. thermal equilibrium is reached. This is a microscopic manifestation of the second law of thermodynamics, and as you can see, everything works by random processes with no need for any part of the system to have "knowledge" about the other parts.

 

[TobyC]

The reason heat engines need a cold sink is completely down to the 2nd law of thermodynamics, which is effectively equivalent to the statement 'You always need a cold sink'.

More precisely, it says that it is impossible for the only net result of any process to be the conversion of heat to useful work. Something else must also happen, and in the case of heat engines that is the hot sink getting slightly cooler and the cold sink getting slightly hotter.

If this law didn't exist, there would be nothing in principle stopping us from turning the vast amounts of heat energy all around us into practically limitless useful work. It is the 2nd law, not conservation of energy, which imposes the most restrictions on us.

If we were feeling cunning we might try using some sort of refrigerator machine to maintain a cold sink to transfer heat to, but this too is not allowed, so another way of stating the 2nd law is by saying that it is impossible for the only net result of any process to be the transfer of heat from a cold body to a hotter body. Something else must also happen, and in the case of refrigerators that is useful work being converted to heat, and you always have to do more work to run the refrigerator than you could get out by running your heat engine.

So heat engines and refrigerators are effectively inverses of each other. You cannot get work from heat without doing something to reduce temperature differences, and you cannot increase temperature differences without doing something to turn useful work to heat. In any such process it is possible to define a certain quantity dependent on heat and temperature which always increases, and this quantity is called the 'entropy'.

Now you suggested that this law seems to place quite heavy restrictions on what can actually happen in any given thermodynamical process, and it does. Things seem to 'know' what to do to stop us humans from tapping into limitless energy, and there is always a universal accountant making sure that the entropy is always going up.

Although from the point of view of our energy requirements these restrictions are very bad, from the point of view of physics they are incredibly useful. The whole subject of thermodynamics is the application of these restrictions to certain processes, so that rules describing them can be discovered.

For example, if you start from the assumption that the energy of an ideal gas depends only on its temperature and not its volume (since there are no intermolecular forces in an ideal gas) then you can use the 2nd law to arrive at a precise description of how the pressure, volume, and temperature of the gas must depend on one another, because if they depended on one another in any other way, it would be possible to construct a heat engine which violated the 2nd law.

You can even do the same thing with light, since light in a container will exert a pressure on it, it too could be used in a heat engine, and it too must therefore behave in a specific way which doesn't allow us humans to get free energy. You can use this to show that the rate of energy radiated per unit area of a hot body emitting radiation, is proportional to the fourth power of its temperature.

You also asked why the world is like this. Originally, the laws of thermodynamics were arrived at from experiment, but with the development of statistical mechanics we now have a good understanding of why the entropy of the universe can only go up, and therefore of why heat engines always need a cold sink. Its because statistically the entropy corresponds to a function of the number of ways you can arrange the microscopic components of a system without changing its macroscopic properties. Macroscopic states with higher entropies are therefore more likely than states with low entropies, and as the universe advances in time it goes to more likely states, simply because of the laws of probability. Initially we must have started off in a very unlikely state with very low entropy, and we don't why that is, but the fact that we did explains why as we move away from that point the entropy is always going up.