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Thermodynamics - Mass on Vertical Piston

  1. Sep 24, 2015 #1
    I keep getting this question wrong, and I am struggling to understand why this is.
    1. The problem statement, all variables and given/known data
    image.png
    2. Relevant equations
    F = p*A
    Ap = π*r2

    3. The attempt at a solution
    Denoting patm as atmospheric force, and p0 as pressure inside the cylinder.

    Firstly, a force balance on the system. Force UP = Force DOWN.
    p0*Ap = m*g + patm*Ap

    patm = 101.4 kPa , and at 104.4°C p0 is equal to a pressure between 110 kPa (at 102.3°C) and 120 kPa (at 104.8°C).

    By interpolation p0 is equal to 118.4 kPa.

    Rearranging the force balance, m = ((p0-patm)*Ap)/g = ((118.4-101.4)*(π*(0.042)2)/9.81 = 0.00960 kg.

    This seems like a VERY unrealistic situation considering this very small mass is creating 17 kN/m2 of force..

    Any help would be appreciated.
     
  2. jcsd
  3. Sep 24, 2015 #2
    I think I realized my mistake, I need to times my mass by 1000 due to using kN/m2 = kPa I should be finding mass with N/m2.

    Edit still wrong...
     
  4. Sep 24, 2015 #3
    The area of a circle is πD2/4, not πD2.

    Chet
     
  5. Sep 24, 2015 #4
    Sorry Chester, I changed the 84mm diameter into 0.042m radius when I put it into the formula.

    It seems my working is correct, except the quiz I'm doing is playing up. Which is really confident battering :/
     
  6. Sep 24, 2015 #5
    Sorry, my mistake. I rechecked your calculation, and it looks correct. But the requirement of 3 significant figures is an issue. If you interpolate in your pressure table, you get 118.4. But if I interpolate in my pressure table, I get 117.9; and if I interpolate in my temperature table, I get 118.0. (I did these interpolations using semi-log interpolation). So the pressure difference can be anywhere from 17 to 16.5.

    Chet
     
  7. Sep 26, 2015 #6
    As always, appreciate your help Chester. In the end it worked out to be correct!
     
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