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Thread: Let's do a Thought Experiment !

  1. #41
    orthogonal

    I hope this doesn't constitute a flaw...

    Does everyone in this thread agree that by merely doubling the earth's atmospheric pressure at sea level, the normal negative pressure-with-altitude gradient due to gravity will remain unchanged?

    There are at least two other variables that change in the atmosphere when it's doubled. One is temperature and the other is volume. Boyles law states that the product of the volume and pressure will remain constant if the temperature remains constant. Law of Charles and Gay-Lussac states that for a gas at constant pressure, the volume is proportional to the absolute temperature. Increasing the volume raises the temperature proportionaly.


    We are left with a tall sealed vertical cylinder containing twice the air pressure than exists in the surrounding atmosphere.

    Not really. You've taken a 'slice' of a much larger system, enclosed it and then decreased the volume of the larger system. The system inside is not aware of the outside systems change in volume. It doesn't have to be. And since there has been no change in the volume or temperature inside of the cylinder, a state of pressure, inside the cylinder, does not exist.

  2. #42
    Registered Senior Member
    Posts
    579
    Thanks for the response Flamethrower,

    Good first point! It would have been less ambiguous had I stated that the atmospheric pressure was to be raised and lowered by way of an isothermal compression followed by an isothermal expansion. This is simple enough to produce in our thought experiment; just include a gigantic heat exchanger to maintain the average temperature of the earth's atmosphere in thermal equilibrium as we alternately pressurize and depressurize the earth's atmosphere. Now we may safely ignore any thermal aspects of this problem.

    As for the volume; let's agree that the overall volume of our atmosphere stays the same when increase or decrease the earth's overall pressure. If it helps, imagine that the boundary between our atmosphere and outer space is sheathed in a thick walled steel sphere.

    I do not understand your second objection. But let me make an analogy. I work on the top of a 4000 foot mountain in Vermont. I have a liter size plastic soda bottle that I normally use to carry water down the mountain in. I normally put the cap on this empty soda bottle at the base of the mountain. When I take it out of my backpack at the top of the mountain I invariably find its walls blown up like a stiff balloon.

    Think of my putting the cap on the soda bottle at the mountain base as analogous to our placing the lid on our very-long-cylinder while immersed in an artificially high-pressure atmosphere. And think of my distended empty soda bottle on the top of the mountain as analogous to the very-long-cylinder surrounded by an atmosphere that has been reduced back to normal.

    The reason I find my soda bottle swollen outward on top of the mountain is that the air inside the bottle is captured while the bottle is immersed in a higher pressure local atmosphere at the mountain base. The bottle would become exactly as swollen while remaining at the base of the mountain if I simply engage my colossal (imaginary) air compressor to transfer enough air out of our earth's atmosphere so that the atmospheric pressure at the base of the mountain is reduced to the pressure normally found at the top of the mountain.

    I hope this analogy helped,
    Michael
    Last edited by orthogonal; 02-09-02 at 09:47 PM.

  3. #43
    orthogonal

    Yes, I understand the analogy. I made reference to the inside system of the cylinder not knowing the lack of atmospheric pressure outside the system because the assumption was that the cylinder walls were rigid while the soda bottle container is probably not.

    If you open up the cylinder, the doubled air inside should come out and dissipate thruout the atmosphere (or lack thereof).

    This is simple enough to produce in our thought experiment; just include a gigantic heat exchanger to maintain the average temperature of the earth's atmosphere in thermal equilibrium as we alternately pressurize and depressurize the earth's atmosphere. Now we may safely ignore any thermal aspects of this problem.

    As for the volume; let's agree that the overall volume of our atmosphere stays the same when increase or decrease the earth's overall pressure. If it helps, imagine that the boundary between our atmosphere and outer space is sheathed in a thick walled steel sphere.


    This will be difficult considering what happens to gas when you start to change the variables.

    Boyles law can be expressed as P1*V1 = P2*V2

    V1 is the original volume
    V2 is the new volume
    P1 is original pressure
    P2 is the new pressure

    Charles law can be expressed as V/T = constant

    V is the volume
    T is the absolute temperature (measured in Kelvin)

    Charles's Law can be rearranged into two other useful equations.

    V1 / T1 = V2 / T2

    V1 is the initial volume
    T1 is the initial temperature
    V2 is the final volume
    T2 is the final temperature

    V2 = V1 (T2 / T1)

    V2 is the final volume
    T2 is the final temperature
    V1 is the initial volume
    T1 is the initial temperature

  4. #44
    Registered Senior Member
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    579
    Flamethrower,

    I don't understand your objection. You are saying that due to Boyle's and Charles' laws, it would be difficult to isothermally increase the internal pressure of a container of fixed volume by pumping air into it. But it's actually quite simple; hold the volume constant in Boyle's equation, and you see that P2 will equal P1. Hold the temperature constant in Charle's equation, and you see that P2 will equal P1. By maintaining a constant volume and temperature, the pressure of a gas is proportional to the number of gas molecules in a given system.

    Part of my job is to lash steel flasks containing nitrogen at high pressure to a sled, and haul them up the mountain behind my snowmobile. We use these flasks to maintain a small positive pressure of nitrogen in the transmission line from our television transmitter to the antenna. The pressure of these "filled" flasks is 2300 psig. Do you think that Charle's law is telling us that the high internal pressure temperature of this flask implies that the internal temperature must always remain high? Let me assure you, these flasks are stone cold! The multistage compressor used to fill these tanks was fitted with a cooler after each stage of compression. These interstage coolers attempt to economically maintain an overall isothermal system compression. The cooling fins you see on an air compressor are there for the same reason.

    My scheme for doubling the average pressure of the earth's atmosphere is no different than the flask of nitrogen. Simply employ a heat exchanger to hold a constant temperature in the fixed volume containing our atmosphere.

    Do you find this explanation satisfactory?

    Michael
    Last edited by orthogonal; 02-10-02 at 06:29 AM.

  5. #45
    Registered Senior Member
    Posts
    220
    The hamster view: Temperature is proportional to gas kinetic energy and that is proportional to the square of the molecule velocity (in a statistical sense). Pressure is proportional to the change in molecular momentum and varies with the molecule velocity. So isothermal pressurization requires that the average molecule velocity decrease. Adding more molecules does increase the pressure (though not linearly if done isothermally).

    The cylinder may be isothermally pressurized but will require more gas than if the temperature were allowed to rise as the gas density increases.

    (Lest one lose sight of the original point of disagreement in Scaevola's thought experiment, this hamster contends gravity does cause a pressure gradient.)

  6. #46

    you're all over thinking it

    it the cylinder is pressurized at a a sea level horizontal then when its vertical it reaches the height of mount Everest would nothing change in side the cylinder. like if the cylinder is air tight how would the pressure change. height is not a factor if it can reach any height, the author could have said the moon for goodness sake and it would still not have affected the thought experiment.

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