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Thermodynamics: Show that the two relations give Pv = RT

  1. Oct 1, 2012 #1
    1. The problem statement, all variables and given/known data

    For an ideal gas the slope of an isotherm is given by

    (∂P/∂v) constant T = -P/v

    and that of an isochore is

    (∂P/∂T) constant v = P/T

    Show that these relations give Pv = RT

    2. Relevant equations

    Pv = RT

    3. The attempt at a solution

    I have never worked with partial derivatives before encountering this problem so I am unfamiliar with the rules and operations involved. I tried setting them equal, adding them to each other but I just don't know where I am going.
     
  2. jcsd
  3. Oct 1, 2012 #2
    You can treat each of the equations as an ordinary differential equation where the independent variable is V and T respectively. When you solve them, you will have two constants. But these constants must be then functions of the "constant" variable, T and V respectively. Then you should be able to find those functions and get the ideal gas law.
     
  4. Oct 3, 2012 #3
    Ok so I got up to this step.

    dP = -P/v dv + P/T dt

    Im unsure of how to proceed from here
     
  5. Oct 3, 2012 #4

    vela

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    Divide by P and then integrate.
     
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