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Homework Help: Isothermal Expansion

  1. Sep 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Let P2 = 10^6 N/m^2, P1 = 4X10^5 N/m^2 and v = 2.5m^3/kmole Find the specific volume v2.
    2. Relevant equations
    Isothermal process, ideal gas. There is also a picture but it's just a generic P = constant/V plot.

    3. The attempt at a solution
    The volume given is the specific volume, so when using the ideal gas law I have to convert from kmoles to moles and make sure I have my n value in the correct place.
    I've tried to use the first law of thermodynamics:
    d'U = d'Q + d'W
    d'U - d'W = d'Q
    PdV = Q = nRTdV/V
    I get stuck here because once I take the integral I get the v I am looking for, but I don't know what goes on the other side of the equal sign. I don't have a specific heat or an identity for this ideal gas and I'm not sure what to do with the Q.

    I've also tried using the ideal gas law P1V1/n = P2V2/n
    But I keep getting values of v2 that are smaller than v1
  2. jcsd
  3. Sep 15, 2016 #2
    You can't use the first law to solve this problem. The ideal gas law is the way to go. Why do you feel that getting values of v2 that are smaller than v1 is incorrect?
  4. Sep 15, 2016 #3
    Mostly that when I use then in the next part of the problem I get a negative temperature in kelvin.
  5. Sep 15, 2016 #4
    The system is isothermal, which you already accounted for with the ideal gas law. So how could the temperature come out negative?
  6. Sep 15, 2016 #5
    Well I didn't include thus because it wasn't part of this part of the problem. The isotherm has a box drawn around it to represent a cyclic process. An isobaric expansion, an isobaric compression, an isochoric increase in pressure and an isochoric decrease in pressure. I'm looking at the isobaric expansion portion
  7. Sep 15, 2016 #6
    Well then, all I can say is that the answer to the problem that you posed is 1.0 m^3. This is obviously a compression rather than an expansion.
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