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I Solving for temperature and volume of Dietrici Equation

  1. Oct 27, 2016 #1
    Hi, guys! I came across hard stuff today. I really hope you can help a poor little worm like me. How do you solve for v & T correspondingly for equation like this⇒p = [RT/(v-b)]e^(a/vRT)?
    What's the technique? How do you call it?
     
  2. jcsd
  3. Oct 27, 2016 #2

    Charles Link

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    The exponential can be expanded (Taylor series) ## e^x=1+x +x^2/2+... =1+x ## for small ## x ## . Normally, iterative techniques work well in solving this type of equation. To first order ## v=RT/p ##, etc. You take this ## v ## and write out the solution for ## v ## on the left with higher order terms on the right side of the equation. Then you get an improved answer for ## v ## and cycle it around again, etc. Also ## v-b=v(1-b/v) ## etc. The ## 1/(1-b/v) ## can stay on the right side and bring the ## v ## to the left...You can even write ##1/(1-b/v)=1+(b/v)+(b/v)^2+(b/v)^3+... ##. (i.e. a geometric series ## 1+r+r^2+r^3+...=1/(1-r)) ##.
     
    Last edited: Oct 27, 2016
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