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

Polytropic Process for an Ideal Gas

  1. Oct 14, 2013 #1
    Hi,

    I have a general question about polytropic processes when working with an ideal gas.

    A polytropic process is one for which PV[itex]\gamma[/itex] = constant.

    What I am wondering is if we assume that n is constant, does that mean that the temperature does not change for the process?

    I see that PV[itex]\gamma[/itex] = nrT = constant, but for some reason it doesn't seem right that a polytropic process would be equivalent to an isothermal process if the number of moles of the system doesn't change.

    A little light on the subject would be great.

    Thanks,

    -Luna
     
  2. jcsd
  3. Oct 15, 2013 #2

    DrClaude

    User Avatar

    Staff: Mentor

    No. A good example of such a process is adiabatic expansion/compression, for which ##T## changes.

    That equation is only valid if ##\gamma = 1##. Otherwise, there is no simple relationship between ##PV^\gamma## and ##T##.
     
  4. Oct 18, 2013 #3
    Ok this concept finally sunk in.

    PV[itex]\gamma[/itex] does not equal nRT unless [itex]\gamma[/itex]=1. So a polytropic process in no way implies that nRT is a constant (even when n is constant).

    DrClaude, thanks for the input!
     
  5. Oct 20, 2013 #4

    DrClaude

    User Avatar

    Staff: Mentor

    Another thing to consider that might be helpful for your understanding:

    Consider a process for an ideal gas where ##PV^\gamma = \textrm{const.}##. Using the ideal gas law, ##PV=nRT##, we have
    $$
    \begin{align}
    P_iV_i^\gamma &= P_fV_f^\gamma \\
    \left( \frac{n R T_i}{V_i} \right) V_i^\gamma &= \left( \frac{n R T_f}{V_f} \right) V_f^\gamma \\
    T_i V_i^{\gamma - 1} &= T_f V_f^{\gamma - 1}
    \end{align}
    $$
    or ##TV^{\gamma - 1} = \textrm{const.}##
    Obviously, if ##V## changes during the process, then ##T## changes (except if ##\gamma = 1##).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Polytropic Process for an Ideal Gas
  1. Polytropic processes (Replies: 2)

  2. Ideal gas processes (Replies: 3)

Loading...