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Equations of state -- Partial derivatives & Expansivity

  1. Mar 12, 2015 #1
    1. The problem statement, all variables and given/known data

    Show that the coefficient of volume expansion can be expressed as

    β= -1÷ρ (∂ρ÷∂T) keeping P (pressure) constant
    Where rho is the density
    T is Temperature
    2. Relevant equations
    1/v =ρ
    β= 1/v (∂v÷∂T) keeping P (pressure ) constant

    3. The attempt at a solution
    I started with the original equation (β= 1/v (∂v÷∂T) ) ,substituted ρ for 1/v and got stuck . What should I do next? What's the solution?

    Thank you!
     
  2. jcsd
  3. Mar 12, 2015 #2

    Bystander

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    "Stuck" where?
     
  4. Mar 12, 2015 #3
    Here, β= ρ(∂v÷∂T)
     
  5. Mar 12, 2015 #4

    Bystander

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    You're using "ρ = 1/v," so what's the next step?
     
  6. Mar 12, 2015 #5
    I don't know :( ...Should I change the partial derivative to 1/(∂T÷∂v) ?
     
  7. Mar 12, 2015 #6
    May I suggest you use the chain rule of derivatives since V=1/rho=(rho)^-1. Take the derivative of the outside function times the derivative of the inside.
     
  8. Mar 12, 2015 #7
    If v = 1/ρ, then, in terms of ρ and dρ, dv = ??

    Chet
     
  9. Mar 17, 2015 #8
    I got it! Thank you :)
     
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