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Is this correct? - Gas Law Question

  1. May 5, 2008 #1
    Is this correct? -- Gas Law Question

    1. The problem statement, all variables and given/known data

    cylinderpressure.jpg
    The cylinder in the figure has a moveable piston attached to a spring. The cylinder's cross sectional area is 10 cm^2 and it contains .005 mol of gas. The spring constant is 1500 N/m. At 16 degrees Celsius, the spring is neither stretched nor compressed. How far is the spring compressed when the gas temperature is raised to 160 degrees Celsius?


    2. Relevant equations



    3. The attempt at a solution

    P1/T1 = P2/T2

    16 degrees C = 289 K 160 degrees C = 433 K

    10cm^2 * (1m/100cm)^2 = .001 m^2

    Since the spring is not exerting any force on the piston initially, the pressure inside the cylinder is equal to the air pressure (1 atm = 101300 Pa)

    (101300 Pa)/(289K) = P2/(433 K)

    P2=151775 Pa and P2= (1500N/m)x/(.001 m^2) + (101300 Pa)

    x=.034 m = 3.4 cm
     
  2. jcsd
  3. May 6, 2008 #2

    alphysicist

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    Hi bcjochim07,

    This expression applies for cases when the volume is constant; I think you'll need to use the form with the volumes in it.
     
  4. May 6, 2008 #3
    Oh yeah, how could I forget?

    So the initial volume can be found:
    PV=nRT (101,300 Pa)(V1)=(.005mol)(8.31)(289 K)
    V1= .0001185 m^3

    P1V1/T1 = P2V2/T2 P2= 101300 Pa + (1500N/m)x/.001 m^2 and
    V2= V1 + Ax where A is the area of the end of the cylinder
    V2= .0001185m^3 + (.001m^2)x

    (101300 Pa)(.000185 m^3)/(289K) = (101300 Pa + 1500x/.001 m^2)(.0001185 + .001x)(1/433K)

    .0648 = (101300 + 1500000x)(.0001185 +.001x)(1/433)
    .0648 = -.0368 + .644 x + 3.46x^2

    [-.644 +/- sqrt (.92)]/6.92

    x= (-.644 + 1.03)/6.92 = .0455 m = 4.55 cm
     
    Last edited: May 6, 2008
  5. May 7, 2008 #4
    Is this correct?
     
  6. May 7, 2008 #5

    alphysicist

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    I think you have a few errors here.

    On the left hand side you have the wrong volume (you're missing a one) that gives the wrong answer on the left side of the next line.

    I think you also made a calculation error in going between these two lines on the right hand side. The right hand side of (101300 + 1500000x)(.0001185 +.001x)(1/433) has all positive numbers, but you got a negative number on the next line.
     
  7. May 7, 2008 #6
    Ok, let's see if I can get it right

    (101300Pa)(.0001185 m^3)/(289K) = (101300 Pa + 1500x/.001 m^2)(.0001185 m^3 + .001x)(1/433K)

    .0415 = (101300 + 1500000x)(.0001185 + .001x)(1/433)
    .0415 = (12.00 + 101.3x + 177.75x + 1500x^2)(1/433)
    .0415 = 3.46x^2 + .234x + .4105x + .0277
    0 = 3.46x^2 + .644x - .0138
    [-.644 +/- sqrt (.606)]/6.92
    x= .0194 m = 1.94 cm
     
  8. May 8, 2008 #7
    Is that right?
     
  9. May 8, 2008 #8

    alphysicist

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    That looks right to me.
     
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