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Ideal Gas Law - Differential Approximation due to variable increase in %.

  1. Oct 29, 2011 #1
    1. The problem statement, all variables and given/known data
    This is a problem form my calculus book, which states:

    According to the ideal gas law, the pressure, temperature, and volume of a confined gas are related by P=kT/V, where K is a constant. Use differentials to approximate the percentage change in pressure if the temperature of a gas is increased 3% and the volume is increased 5%.

    3. The attempt at a solution

    Here, I include my original attempt at the solution and a solution that I found online. In my original solution, I found the answer to be 2%, but the solution says 4%. I'm not sure why... but I think it's related to something I don't understand in the actual solution, where it seems to me, they divide by 1/2 for no apparent logical reason.

    Could someone please explain to me where my logic is flawed?
    attachment.php?attachmentid=40470&d=1319929174.jpg

    Here is a solution I found online to the same problem, perhaps it's more clear.
    attachment.php?attachmentid=40468&d=1319927946.jpg
     

    Attached Files:

    Last edited: Oct 29, 2011
  2. jcsd
  3. Oct 29, 2011 #2
    Edited to make images easier to see. (Sorry.)
     
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