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Old person curious about conservation of energy

  1. Dec 14, 2009 #1
    I have come to this forum to see if someone can explain the following in non-mathematical terms.

    I board a steam train in Yorkshire and travel to London. I understand that energy is in the coal, which is burned and transforms some of the energy into heat which raises the steam which drives the pistons. Along the way some energy is distributed as friction and I am transported from Yorkshire to London. If energy is neither created nor destroyed where does the original energy in the coal now reside and in what way can I understand it being available for further transformation? I think that my presence in London represents a transformation of an amount of energy but where is it? Is this what is meant by entropy?

    Lets say that the train crashed into a bridge so it's momentum caused the transformation of the train and bridge into twisted metal and rearranged bridge materials. Where is that energy now?

    This is probably elementary stuff but I would like to understand it.
  2. jcsd
  3. Dec 14, 2009 #2

    That's basically the answer you are looking for, when you burn the coal you produce useful heat (to increase the temp of the water in the boiler), and wasteful heat (one that heats the surroundings and not the water in the boiler).

    From this transfer of heat, mechanical energy is harnessed (by the piston) and useful work is done (the train moves). As you say friction and other losses also occur which is also lost as heat. In the end all heat ends up in the surrounding area.

    In the second case, the energy is still ultimately dissipated as heat into the surroundings. However the 'useful' work done, is used not to propel the train to london but to twist metal. The metal acts like a spring, you give it some elstic energy, then deform it plastically (so it wont go back to its original shape) all of this energy heats the metal, this heat is then dissipated into the surroudings.

    For example when you repeatedly bend a peice of metal it will get hot, from intenal friction.

    This is more an example of the 1st law of thermodynamics. It says that all energy will just be shifted from one form to another. The 2nd law is slightly more tricky to imagine, the 2nd law conerns entropy and it says that in a heat cycle (in this case a steam engine - Rankine cycle) not all energy is availabe to do work. So within the peice of coal, a certain amount of energy will be lost regardless on its conversion to heat.

    Hope that helps, if there is something that's not really clear just let me know and i'll have another go.
  4. Dec 14, 2009 #3
    Most of the energy released by burning the coal went up the stack (about 2/3 of it). The portion that went into driving the train went into pushing the air out of the way to let the train pass. Some of it went into heating up the rails as the train went by. Where is it all now? The air and the ground are a little warmer. The wind creasted by the passing train made the leaves on the trees along the track flutter - these leaves and the twigs are a little warmer. The energy isn't really available for further transformation because it exists at a temperature not much higher than the ambient. And yes, this is related to entropy which has to do with "how hot" the material holding the heat is, in relation to the temperature of other bodies we can transfer the heat to.
  5. Dec 14, 2009 #4

    D H

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    A quibble with this last post, emphasis mine:
    Materials don't "hold" heat. The heat flow when a thermodynamic system moves from some point A to another point B in the state description of the system depends on the path between these points. This path dependence means that heat cannot be a state variable. Objects do not "hold" heat. Entropy and temperature are path independent, so these things can be (and are) thermodynamic state variables.

    Back on topic: The energy in the coal goes into increasing the temperature and entropy of the train itself and the surrounding environment.
  6. Dec 14, 2009 #5
    Nobody mentioned that when the train's moving it carries kinetic energy equal to 1/2mv^2
    where m is the total mass of the train and v is its speed.

    So to start the journey a lot of the chemical energy in the coal has gone into making the train move to give it 1/2mv^2 of KE. Of course a lot of energy is used up overcoming friction/air resistance too - so that's just straight to heat. When the train arrives in london, all that kinetic (motion) energy is turned into other forms of energy when the brakes are applied (or when the train crashes). At London the kinetic energy becomes heat and squealing in the trains brakes and railway track etc. Or heat and sound waves in the twisted metal of the crash site.

    Whatever happens along the journey energy isn't lost anywhere, it just transforms into different types. And all came out of the coal.

    Instead of mechanical brakes at London, the train could use some form of electric generator or whatever to turn the 1/2mv^2 into stored electrical energy that could then be used to get the train moving again. Or it could simply run up a ramp instead of using brakes so the enegy is stored as potential mechanical energy due to being higher up. But usually the 1/2mv^2 is just thrown away as heat.

    DH, how can a train have entropy , and how would you measure it ?
  7. Dec 14, 2009 #6
    I consider equations to be maths (ok its a pretty simple eq) but the OP specifically asked for no maths. It also doesn't really add anything to the explination of how the energy changes, just gives you a quantity.
  8. Dec 14, 2009 #7
    OK, I was being sloppy between "heat" and "energy." The point I was trying to make was the burning coal is at what, several thousand degrees - and we can do useful things with it. After the train goes by, the rails and air and so forth have been raised from 68 to 68.1 degrees - and we can't do much with that.
  9. Dec 14, 2009 #8
    Well you make a valid point there. But you will agree, I think, that as the train moves the 200 miles from Yorkshire to London, we need to keep shoveling in coal to maintain the train's speed. That continued energy use goes into overcoming the friction, and (also not previously mentioned) climbing any hills. Hillclimbing transforms the energy into potential energy (which can be recovered when the train subsequently travels downhill).
  10. Dec 14, 2009 #9


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    Right. The coal's energy came from the sun's light hitting the Earth millions of years ago. This is low entropy energy (all the light is traveling in the same direction and at high frequencies relative to the environmental temperature). If the light just hits the ground it is converted directly to heat which is high entropy energy in the form of random motions of atoms and light. Instead the plants convert much of that energy via photosynthesis to the energy stored as free carbon and atmospheric oxygen. The train later converts that energy to heat by burning the coal.

    Now though the heat in the boiler of the train is higher in entropy than the coal it, still being hotter than the environment, is not at highest entropy. That occurs when this heat is spread as far as possible i.e. in the rails and wind. The engine manages to tap the spreading of the heat to the surroundings and pull off enough mechanical energy to move the train. The higher the difference in temperatures the more efficiently this energy can be separated into work and pure heat.

    It is important to understand that heat and temperature, though related, are not exactly the same thing. Heat is thermal (randomized) energy while temperature is the degree of concentration of that heat. Thus the light coming from the sun, though thermal, is much lower in entropy per unit of energy than the same amount of energy in the hot asphalt when it absorbs sunlight. That heat in turn has less entropy than the resulting infrared radiation spreading back into space.

    Entropy is a measure of the non-uniformity of a quantity (in these examples energy) and for systems in isolation the entropy will always increase toward some maximum. To lower entropy requires you input low entropy energy and dissipate that energy in higher entropy form (heat). This is why we must eat food and the sweat as we work, why cars must have radiators, and why refrigerators must have electrical energy to pull the heat out of their interior. Engines are mechanisms to separate a form of energy (with intermediate entropy) into low entropy and high entropy parts e.g. the turning wheel of a train and the heat expelled from the train's exhaust.

    You can view the Earth as a whole as a type of heat engine fueled by the sun, by residual radioactive material, and a bit by orbital and rotational energy yielding tidal effects. The "radiator" of the Earth is the thermal infrared radiation dissipating out into space.

    The worry about Global Warming and the Green House Effect (though overblown IMNSHO) is analogous to the worry of a clogged radiator in an automobile. Being unable to dissipate as much heat the engine's temperature must increase and it cannot as efficiently yield low entropy energy.

    A final note. Whenever you have a complex system with a flow of low entropy energy in and high entropy energy out there will tend to be what is called self organizing behavior. If the Earth were just black asphalt, air, and sunlight then you'd see storms develop. Throw in water and oceans and you get currents and hurricanes. Throw in chemicals and you get more and more sophisticate reactions driven by the through-flow of energy. The more ingredients you throw in the more the path from low entropy to high entropy energy can become convoluted (like a river's tendency to become more winding). It is in this context that life can, from a thermodynamic perspective, spontaneously form and evolve, ever increasing the efficiency at which the incoming energy gets used.
  11. Dec 14, 2009 #10


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    So it all ends as heat - and you have in fact not added much to the problem, as OP was asking where all this energy is AFTER train get to the final station.
  12. Dec 15, 2009 #11
    Sweep all the clutter :) aside and your left with combustion is the act of a substance (ex. coal) changing to a liquid, then changing to a gas and ignited (as the temperature increases) which then causes air molecule movement to increase and expand increasing pressure. Depending how rapid this occures determines the energy available for work at any given momement. The faster the transformation the more energy available.

    This expansion and increased pressure moves mechanical objects converting potential energy into mechanical energy allowing work to be done.

    Burning the coal transfers heat from the coal consuming it. uncombusted coal goes up the stack as wasted energy in the form of smoke. energy is transfered from the coal by heat to the water (work is being done thus temperature loss) into steam which expands the air and increases pressure in the confined area except for a movable piston which transfers the heat energy into the mechanical energy of wheels turning driving the train.

    Basicall potential energy is converted to knetic energy thru heat transfer.
  13. Dec 15, 2009 #12


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    The question is - what have happened to this kinetic energy. And the answer was already given several times.
  14. Dec 16, 2009 #13
    All materials to give off heat as energy must be converted to a gaseous state. Ask any fireman. Solid, to a liguid, to gaseous, to combustion. now using this energy build-up thru heat utilizing this to do work, weather moving a train trhu mechnacial energy or moving leaves thru creating pressure changes in the air.

    You don't need heat to created this energy. Cold will do this. Freeze a water filled enclosed pipe will burst giving off energy. Pour water into a crack in concrete and watch the cold air (dissapating heat move the concrete slabs.

    Amy I stateing the same thing you are?
  15. Dec 16, 2009 #14


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    Piece of pure carbon (and I don't mean coal, but carbon) burns and converts to gas without becoming liquid. In teh case of coal this a little bit more complicated, as coal is not pure carbon, but contains substances that will go through the liquid phase - their amount is not constant and depends on the coal type.

    Moving train or moving leaves is not the FINAL state. Final state is when train and leaves stopped to move. Where is the energy now?
  16. Dec 16, 2009 #15

    Freezing something requires an energy flow, that energy flow is called heat.

    Ultimately every single thing ends up as heat. This is what the OP wanted to know.
    Chemical Potential -> Mechanical (kinetic) -> Heat
  17. Dec 16, 2009 #16
    The energy your train used is conserved. Where is it now? After all, the energy that got you to London in the first place seems nowhere to be seen! It's as if the energy that got you to London just came and went: It came in the form of heat to drive the train, then went somewhere, never to be seen again.

    But the truth of the matter is that the energy is to be seen again! It's now seen exiting the solar system at the speed of light as thermal radiation--a different form of energy than the lump of coal that brought you to London.

    Now if you can find some way of going outside the solar system and reacquire all that thermal radiation that the train's boiler radiated away, and somehow find a way to concentrate it and focus it all back on the boiler of that train, then that train can go back from London to Yorkshire on that thermal radiation alone.
  18. Dec 17, 2009 #17
    Unless the train comes to rest in a station at an elevation higher than the station it left from. Then some of the energy 'ends up' as gravitational potential in the train.

    The point of thermodynamics is you can't reacquire 'all that thermal radiation' - real systems are not reversible.
  19. Dec 17, 2009 #18
    If there is conservation of energy there is no final state only constant states of change. In the case you mentioned the available energy from the coal is depleted by moving objects and changing temperaturers.
  20. Dec 17, 2009 #19
    The mechanical potential is just a holding stage until it turns to heat. Stopping it at a higher or lower point is arbritrary, had it just rolled down a big hill it would have 'lost' a load of energy. Absolutely everything will end up as heat if you give it long enough. On a universal scale everything will lead to heat.

    And because of....

    Will lead to heat death. (assuming a closed universe)
  21. Dec 17, 2009 #20


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    I think it is clear from the opening post what is meant by final state in this particular case.

    So we are back where we started. I have a cup of tea on my desk right to my keyboard. I have moved it to the new position left to my keyboard. I have expelled some energy to move the object, but energy of the object have not changed. Where is this expelled energy right now?
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