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IDeal gas law

  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 6.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C.


    I searched for a similar question however I didnt understand it. Maybe it was the calculation error. Someone help me....

    2. Relevant equations

    PV = nRT
    [PV/T]i = [PV/T]f
    Volume of cylinder = Ah


    3. The attempt at a solution

    First I convert my units. Initial state: 101325 Pa, 293 K, and 0.006 m^3
    I determined the constant by using the gas law PV/T. (101325)(0.006)/293 = 2.0749 [(Nm^2)/K].
    After the temperature is increased to 503 K (273+230), the piston rises and the volume changes. The new volume is 0.006 + Ah = 0.006 + 0.01h. The pressure is equal to P = F/A. F is the force constant times dispalcement (h), which is 2000 N/m. P = 2000/0.01 = 200000h N/m^2.
    Putting everything together we get
    2.0749 = (200000h)(0.006+0.01h)/503

    The answer h = 0.482 m or 48.2 cm is incorrect. Any suggestion or corrections. Thank you.
     

    Attached Files:

    Last edited: Nov 30, 2006
  2. jcsd
  3. Nov 30, 2006 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    You have to develop the equation for pressure:

    [tex]P_f = P_i + kh/A = nRT_f/V_f[/tex]

    Since [itex]P_i = nRT_i/V_i[/itex], and [itex]V_f = V_i + Ah[/itex]

    you should be able to work that out for h.

    AM
     
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