1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The temperature change of an ideal gas, Joule Kelvin expansion (const. enthalpy)

  1. May 4, 2012 #1
    1. The problem statement, all variables and given/known data

    This is the last part of the question. So far have been made to derive:

    ## \mu _{\text{JK}}=\left(\frac{\partial T}{\partial P}\right)_H=-\frac{1}{C_P}\left(\frac{\partial H}{\partial P}\right)_T ##

    Then

    ##\left(\frac{\partial H}{\partial P}\right)_T=V - T \left(\frac{\partial V}{\partial T}\right)_P ##

    It says you need to derive an expression for the temperature change as an integral over pressure.


    3. The attempt at a solution

    ##dT=\left(\frac{\partial T}{\partial P}\right)_HdP+\left(\frac{\partial T}{\partial H}\right)_PdH ##

    At constant enthalpy ## dH = 0 ##.

    ## dT=\left(\frac{\partial T}{\partial P}\right)_HdP\text{=}-\frac{1}{C_P}\left(V-T\left(\frac{\partial V}{\partial T}\right)_P\right) ##

    So I think the change in temperature will be:

    ## \text{$\Delta $T} =-\frac{1}{C_P} \int_{P_1}^{P_2} \left(V-T\left(\frac{\partial V}{\partial T}\right)_P\right) \, dP ##

    Then it says derive an expression for the temperature change for an ideal gas.

    ## p V = n R T ##

    ## V = \frac{ n R T}{P} ##

    ## T\left(\frac{\partial V}{\partial T}\right)_P = \frac{ n R T}{p} ##

    So it would seem the integral vanishes, and ## \Delta T = 0##

    I don't think this is right.
     
  2. jcsd
  3. May 6, 2012 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Oh, but it is. The Joule-Kelvin coefficient μJK for an ideal gas is identically zero.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: The temperature change of an ideal gas, Joule Kelvin expansion (const. enthalpy)
Loading...