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Isothermal expansion

  1. Sep 19, 2005 #1
    If air has a pressure of 40 psig and a volume of 8 cu. ft. expands isothermally to a pressure of 10 psig, find the external work performed during the expansion. How do I do this, do I first have to change 40 psig to psia, and how do I do that? This question has me lost! Any help appreciated, even a formula for me to understand it would help. thank you
     
  2. jcsd
  3. Sep 20, 2005 #2

    Andrew Mason

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    Use PV=nRT.

    If T is constant then [itex]P_iV_i = P_fV_f[/itex]. So you can work out what the final volume is.

    The work is:

    [tex]W = \int_{P_i}^{P_f} PdV = \int_{V_i}^{V_f} \frac{nRT}{V}dV [/tex]

    You have to work out that integral (hint: [itex]\frac{d}{dV}ln V = 1/V[/itex]) and plug in the initial and final volumes.

    You don't have to do any conversions. You just need the pressure ratio P_f/P_i.

    AM

    [edit: this last comment is not quite correct. You do have to work out nRT = P_iV_i which means you have to do a conversion. PSIA is absolute pressure in pounds/in^2, which means you have to include atmospheric pressure. PSIG is gauge pressure, which is 1 atm less than actual. It is easier to work in MKS. I would convert to MKS and then convert back.]

    AM
     
    Last edited: Sep 21, 2005
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