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Gases and Pressure

  1. Nov 30, 2006 #1
    1. The problem statement, all variables and given/known data

    An expandable cylinder has its top connected to a spring with force constant 2.00 103 N/m. (See Fig. P10.58.) The cylinder is filled with 4.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C.

    [​IMG]

    (a) If the lid has a cross-sectional area of 0.0100 m2 and negligible mass, how high will the lid rise when the temperature is raised to T = 230°C?


    (b) What is the pressure of the gas at 230°C?



    2. Relevant equations

    PV=nRT
    PiVi/Ti= PfVf/Tf


    3. The attempt at a solution

    Ok I did Pf= Pinitial+ k(spring constant)(h)/Area
    Also Vf= Vi + h(Area)

    Then I plugged these into the PiVi/Ti= PfVf/Tf
    and its not the right answer

    What am I doing wrong?
     
  2. jcsd
  3. Nov 30, 2006 #2

    berkeman

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    Looks reasonable at first glance. Can you show your math with units so we can check?
     
  4. Nov 30, 2006 #3
    ((1.013X10^5 Pascals)(.004m^3))/20 Celsius= (((1.013X10^5 Pascals + 2X10^3N/m X height)/0.0100 meters^2)(.004m^3 + 0.0100meters^2 X height))/all over 230 Celsius
     
    Last edited: Dec 1, 2006
  5. Nov 30, 2006 #4

    berkeman

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    I guess I was looking for a more step-by step development, but whatever. Where is the 1atm of initial pressure again? What units are you using? Be sure to include *all* units to be sure that they are consistent.
     
  6. Nov 30, 2006 #5
    the 1 atm of pressure= 1.013X10^5 Pascals

    I edited it to include the units
     
  7. Nov 30, 2006 #6

    berkeman

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    Are Pascals, ml, N and m all compatible units? What are the base units of Pascals? (Sorry, I don't know offhand)

    It looks like in the first part of the righthand side, you are mixing units of Pascals = N? How can a pressure equal a force? Do you see what I mean about carrying your units along to help you check your equations and manipulations? And near the end there, it looks like you are saying that a ml = m^3?
     
  8. Nov 30, 2006 #7
    1 Pa ≡ 1 N/m²

    let me convert the ml to m^3, maybe thats the problem
     
  9. Nov 30, 2006 #8

    berkeman

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    Remember, in order to add terms, they have to have the same base units. And the left and right hand sides of an equation must have the same base units....
     
  10. Nov 30, 2006 #9
    I am doing something wrong, I am not getting it right
     
  11. Nov 30, 2006 #10

    berkeman

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    Re-write the equation, being careful to keep your units consistent as I mentioned in post #8. I have to go now. Good luck.
     
  12. Nov 30, 2006 #11
    I dont know whats wrong, its not getting the right answer
     
  13. Nov 30, 2006 #12
    can someone help me and try it and see what I am doing wrong and the answer they get?
     
  14. Nov 30, 2006 #13

    Gokul43201

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    Units for temperature?
     
  15. Dec 1, 2006 #14
    ^ I have it there in Celsius
     
  16. Dec 1, 2006 #15

    berkeman

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    Show us the current version of your equation, with the corrected and checked units, and we'll try to help you. We don't do your work for you.
     
  17. Dec 1, 2006 #16
    ^ I have it written on top but if u want it again

    ((1.013X10^5 Pascals)(.004m^3))/20 Celsius= (((1.013X10^5 Pascals + 2X10^3N/m X height)/0.0100 meters^2)(.004m^3 + 0.0100meters^2 X height))/all over 230 Celsius
     
  18. Dec 1, 2006 #17

    berkeman

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    But the units still look wrong to me, which implies that the equation is not formed correctly.

    lefthand side --> [ Nm^2/C ]

    righthand side --> [ ( ((N/m + N)/m) m^3 )/C ]
     
  19. Dec 1, 2006 #18
    hmm I really dont know what I am doing wrong, this is so frustrating
     
  20. Dec 1, 2006 #19

    berkeman

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    I think the problem is that you are trying to do too much in one line, and are not being careful about the algebra and units. Try it this way:

    What is the answer for PiVi/Ti= ? (show the units of the answer)

    Then set that equal to PfVf/Tf (being careful about the algebra and units) and solve for h.
     
  21. Dec 5, 2006 #20

    Gokul43201

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    I wasn't asking a question; I was giving you a hint!

    Is Celcius the correct unit to describe thermodynamic temperature?
     
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