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Using Ideal Gas Law and Charles Law to compute limit

  1. Jan 28, 2013 #1
    1. The problem statement, all variables and given/known data
    The ideal gas law from chem is PV = nRT. A process carried out at const. pressure is said to be isobaric. A process carried out at const. temperature is said to be isothermal.

    A.) Using limits and the ideal gas law and assuming const. number of moles, show that that the volume of gas in an isobaric process goes to 0 as temperature goes to 0 and that the volume of gas in an isobaric process goes to +∞ as temperature goes to +∞. (Note: this is related to Charles' Law)


    2. Relevant equations
    PV=nRT
    Charles Law: V1/T1 = V2/T2 or V2/V1 = T2/T1 or V1T2 = V2T1



    3. The attempt at a solution

    Should I set this up as to different functions such as Lim x-> 0 f(x) = +∞ and Lim x->0 g(x) = +∞
    Is that way off?

    I'm having a hard time trying to implement the 2 equations.
    In either equation do I need to get a 0 in the denominator as 0+ which goes to +∞?
    This question is tricky for me
     
  2. jcsd
  3. Jan 28, 2013 #2

    Dick

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    V=nRT/P. P (pressure) is constant since it's isobaric, n (moles) is constant since the number of moles is constant. R is always constant. V(T)=constant*T. It's just one function. Now let T->0 and and T->infinity. Where's the tricky part?
     
  4. Jan 28, 2013 #3
    Are you implying:

    lim t-> 0 (VT = nT)
    and
    lim t->∞ (VT = nT)
     
  5. Jan 29, 2013 #4

    Dick

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    I'm not sure what that means and I'm also not sure what that has to do with what I said.
     
  6. Jan 29, 2013 #5
    Sorry. It's getting late.

    So, are you suggesting simply have V = nRT/P with one being 0 and ∞ ?
     
  7. Jan 29, 2013 #6

    Dick

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    It must be getting late. Yes, V=(nR/P)T. (nR/P) is a positive constant. Think about the limits as T->0 and T->infinity.
     
  8. Jan 29, 2013 #7
    Alrighty..

    Hmm. I'll tell you what I see and I know it's probably way off. But, I need to get my view or approach better for these problems

    What my head is telling me and all I see is that (nR/P) is a positive value and as T approach 0 the value for V is getting smaller. I don't know if this has to do with anything. And vice versa for +∞.

    I guess with these problems, I'm facing problems in regards of comprehending what I need to do or where to start.
     
  9. Jan 29, 2013 #8

    Dick

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    I don't think you are dealing with a 'proof' class where have to show anything. Just say what you think. How small can V get as T->0? How large can V get as T->infinity?
     
  10. Jan 29, 2013 #9
    -∞ with lim t->0 and +∞ with t->+∞
     
  11. Jan 29, 2013 #10

    Dick

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    You can't really think V is near -infinity if t is near 0, can you?
     
  12. Jan 29, 2013 #11
    0 with lim t->0 and +∞ with t->+∞ in regards to V

    V = (nR/P)T
    V= (nR/P) * 0 = V near zero
    -------------------------
    V-(nR/P)T
    V=(nR/P)*+∞ = V near +∞
     
  13. Jan 29, 2013 #12
    Also, if doing the same type of problem but relating the ideal gas law with boyles law P1V1=P2V2 can we show that the volume of gas in an isothermal process goes to +∞ as pressure goes to zero and that the volume of gas is an isothermal process goes to 0 as pressure goes to +∞.
    T is constant= constant
    Moles = constant
    R = constant


    So, V= (nR/P)T

    Lim P->0 V = (nR/0)T --> V goes to +∞
    and
    Lim P->+∞ V = (nR/+∞)T --> V goes to 0
     
  14. Jan 29, 2013 #13

    Dick

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    That sounds better.
     
  15. Jan 29, 2013 #14
    Alright cool, thanks.
     
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