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Energy of compression

  1. Jul 23, 2007 #1
    I am having a problem determining the equation to use here. I want to find the energy to compress hydrogen using a pump from a low pressure to a high pressure. Do I use an isothermal or an adiabatic equation?

  2. jcsd
  3. Jul 23, 2007 #2
    It depends on how your pump is working.

    If it ensure that the temperature is fixed, then it would be isothermal.
    This would be a good model if there was an excellent heat exchange between the gas and the pump, and if the pump itself was maintained at a fixed temperature for example by an efficient cooling system.

    If, on the contrary, we can assume there is only little heat lost from the gas, then it would adiabatic.

    In a real system, it would probably be somwhere in between.
    In a real process there could be still other differences.

    In summary, you have to chose the best model.
    This choice may depend on other information available to you.
  4. Jul 23, 2007 #3
    Thanks for the info the problem is starting to clear up now.
    What's the formula for Isothermal compression?. and would it be isothermal if heat was transfered to the system after or during compression of the gas?

  5. Jul 23, 2007 #4
    The work would be totally different depending on when the heat transfer occurs.
    In gas turbines, approaching an isothermal process leads to efficiency improvements.
    (and the transformation is close to adiabatic too ... no heat losses, both together makes it reversible!)

    The formula to use is the same for all processes:

    Work = integral (dW) = integral (- p dv)

    The difference occurs simply because of path of integration.
    For a perfect gas, you also always have pv=nRT.
    For an isothermal process T is constant.
    For an adiabatic process, the work done heats up the gas: dE = n cv.dT = dW .

    From this you see that the formulas are -in a sense- the same, but the way to use them is different: either T is fixed, or T increases.
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