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Problem with the definition of work

  1. Oct 15, 2006 #1
    Hi all,

    I m having a little problem with the definition of work:

    -Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. Work is a scalar quantity which can be positive or negative.

    -In thermodynamics, thermodynamic work is the quantity of energy transferred from one system to another. It is a generalization of the concept of mechanical work in mechanics.

    ----->now my real problem comes when i take free gas expansion as an example:normaly work should be equal to 0 (thats what i read in books)
    How can that be since we have an expansion DV and obviously a force responsible for that expansion P (pressure).
    In my book it says that work in tha case of free expansion equals to 0 because it defines work as:

    -distance * force resisting to the movement.

    In that case i agree that free gas expansion work equals 0 since there is nothing resisting the expansion, however that third definition is in contradiction with the first one.

    I am so confused.Please help!!
  2. jcsd
  3. Oct 15, 2006 #2


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    Science Advisor

    No, there is no force or pressure in free expansion. Pressure is is the force (divided by area) of the wall or membrane that prevents free expansion. Remove the barrier and the expansion happens as a consequence of the random motion of the molecules making up the gas.

  4. Oct 15, 2006 #3
    indeed..! now i understand better.
    one more question however:

    What should i learn:
    -work=force*distance (my last year book) or
    -work=distance*force resisting to the movement (this years book..)

    ...or is it quantitatively (EXACTLY (?)) the same since if there is little resistance, distance will be longer and if the resistance is greater, distance will be shorter for the same force applied?
    Last edited: Oct 15, 2006
  5. Oct 15, 2006 #4
    To be fair, they are the same, just probably not explained to you in properly. The one you want to learn is the second one because unless you are in a vaccuum, there will always be a resistive force (normally in the opposite direction to motion).

    The Bob (2004 ©
  6. Oct 15, 2006 #5


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    Homework Helper

    You have to consider the work done by the expanding gas. So if the gas expands by applying a force against something, say a piston, energy is removed from the gas in doing work on another system.
  7. Oct 15, 2006 #6


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    Science Advisor

    As long as an object is not accelerating, the net force is 0 so the "resistive force" is the same as the force applied to the object.
    If the object is accelerating, then the work done by the force goes part into overcoming the resistive force and part into increasing the kinetic energy.
  8. Oct 15, 2006 #7
    All of your replies were so helpful !!
    Thank you! I understand better now.

    (could you please get all together and write a book!
    Seriously, i got more out of your 4 posts than i did reading my whole thermodynamics chapter...)
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