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Ideal gas law problem

  1. Aug 29, 2014 #1
    1. The problem statement, all variables and given/known data
    for one mole of an ideal gas this relation holds good
    P= P0 /{1+(V0/V)^2}, where P0and V0 are constants,
    what will be its change in temperature in terms of P0,V0 and R,
    if volume is doubled?


    2. Relevant equations
    for one mole of ideal gas we know PV=RT

    Then RT/V= P0 /{1+(V0/V)^2}

    How to proceed then? Can anyone help, please.


    3. The attempt at a solution
     
    Last edited: Aug 29, 2014
  2. jcsd
  3. Aug 29, 2014 #2

    CAF123

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    Gold Member

    Evaluate the temperature of the gas when it occupies a volume V and 2V using the ideal gas law.
     
  4. Aug 29, 2014 #3
    The Answer given in the text is(11/10) P0V0/R. How shall I reach?
     
    Last edited: Aug 29, 2014
  5. Aug 29, 2014 #4
    According to the equation, if the initial volume is Vi, what is the initial pressure Pi? What is the initial temperature (using the ideal gas law? In terms of Vi, what is the final volume, Vf? What is the final pressure?

    Chet
     
  6. Aug 29, 2014 #5
    If we take initial pressure P0
    and initial volume as V0
    Initial temp = T1
    Final Pressure = P0 (remaining constant)
    final doubled volume =2V0
    and final temp = T2

    then by ideal gas law for one mole of gas
    T2-T1=2P0V0/R -P0V0/R=P0V0/R

    Is this a correct solution? Then what is the utility of the given equation?
     
  7. Aug 29, 2014 #6
    No. If V0 is the initial volume, then, from the equation they gave, P0 is not the initial pressure. As they said in the problem statement, P0 and V0 are just constants for the problem (and are not related to the initial conditions).

    Chet
     
  8. Aug 29, 2014 #7
    for initial vol V0 the initial pressure is P0/2
    for final vol 2V0 the final pressure is (4/5)P0
    Then temperature change becomes =(11/10)P0V0/R

    I think it is correct
     
  9. Aug 29, 2014 #8
    Yes, if the initial volume is V0.

    Chet
     
  10. Sep 5, 2014 #9
    Is it possible to arrive at the same result without having taken the initial volume as V0?
    If possible please suggest a way out.
     
  11. Sep 5, 2014 #10
    It might be. The problem statement sort of implies this. Have you tried, and, if so, how far have you gotten?

    Chet
     
  12. Sep 5, 2014 #11
    I tried but failed to eliminate v1 initial volume to have the required relation. Please give hints if possible.
     
  13. Sep 5, 2014 #12
    I'll give it a shot.

    Chet
     
  14. Sep 5, 2014 #13
    The only initial volume that matches the answer in the text is it is equal to Vo.

    Chet
     
  15. Sep 5, 2014 #14
    So u have reached the same conclusion as I have , Thanks.
     
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