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Thermodynamics: Calculating Pressure Increase From Work

  1. Nov 3, 2017 #1
    1. The problem statement, all variables and given/known data
    Estimate the pressure increase required to impart 1 J of mechanical work in reversibly compressing 1 mol of silver at room temperature. What pressure rise would be required to impart 1 J of work to 1 mol of alumina at room temperature? For alumina take the molar volume to be 25.715 (cc/mol) and (BETA)=8*10^(-7) (atm)^(-1).
    For silver, the molar volume is 10.27 (cc/mol) and (BETA)= 9.93*10^(-6)
    Beta is the coefficient of compressibility

    2. Relevant equations
    Mechanical Work= -PdV
    dV=V(ALPHA)dt-V(BETA)dP

    3. The attempt at a solution
    I assumed that temperature remained constant during this process. I know that the answer should be 9.6*(10)^6 atm for silver and 978 atm for alumina. I have been getting 140041 atm for silver and 311800 atm for alumina. The attempt is attached below. Any ideas as to what I'm doing wrong? Thanks in advance!
    [​IMG]
     
  2. jcsd
  3. Nov 3, 2017 #2
    I can't open your attachment. Have you uploaded the file?
     
  4. Nov 3, 2017 #3
    Sorry, thought I attached the image to the original post

    unnamed.jpg
     
  5. Nov 3, 2017 #4
    I just realized what I was doing wrong. I needed to convert the mechanical work (in Joules) to units of cm^3 atm. This gives me the right answer for alumina, but I'm getting 1461.34 atm for silver. Attached below is the work with the conversions in mind

    unnamed-2.jpg
     
  6. Nov 3, 2017 #5
    This result doesn't seem to agree with your result shown on the paper. Please show your work, including the substitutions.

    I confirm the 979 atm for alumina. For silver, from the data given, I get 440 atm.
     
  7. Nov 3, 2017 #6
    Here's the work for the silver sample, I'm still getting 1461 atm
    unnamed-3.jpg
     
  8. Nov 3, 2017 #7
    It looks like you used the wrong value of beta in your calculation. Otherwise, nicely done.
     
  9. Nov 3, 2017 #8
    Okay, thank you!
     
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