Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Partial differential equations?

  1. Apr 13, 2014 #1
    Hello, PF! As I was reading my P-Chem textbook, I noticed most thermodynamic equations involve partial derivatives, like these ones: [tex]C_V = {\left( \frac {\partial E}{\partial T} \right )}_V[/tex] [tex]{\left( \frac {\partial H}{\partial T} \right )}_P = {\left( \frac {\partial E}{\partial T} \right )}_P + P{\left( \frac {\partial V}{\partial T} \right )}_P[/tex] However, none of these equations is ever actually called a PDE by the author. Is it implied they are PDEs given they involve partial derivatives, or are they not classified as PDEs such as the wave or heat equations? Thanks in advance!
     
    Last edited: Apr 13, 2014
  2. jcsd
  3. Apr 13, 2014 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    They are not equations, but equalities, because there's no unknown function and no boundary conditions. In the first equality you wrote, you should determine what E(T,V) looks like, then partially differentiate wrt T, to get the function C_V(T,V). For the second, there's an equality involving 3 different functions, H(T,P), E(T,P) and V(T,P).
     
  4. Apr 13, 2014 #3
    I get it now, they are not equations in the sense that they need not be solved, right? They are just showing the relation between thermodynamic functions.
     
  5. Apr 13, 2014 #4

    Mark44

    Staff: Mentor

    Right.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Partial differential equations?
Loading...