1. Limited time only! Sign up for a free 30min personal 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!

Prove u= u_f + xu_g and h= h_f + xh_fg

  1. Mar 24, 2015 #1

    I'm learning thermodynamics using the book titled "Thermodynamics An Engineering Approach (5th edition)".
    In page 130, the derivation of v_avg = v_f + xv_fg is shown but how about deriving u_avg= u_f + xu_g and h_avg= h_f + xh_fg ?

    The derivation of the derivation of v_avg = v_f + xv_fg is like this:
    Consider a tank filled with saturated liquid-vapor mixture. Then the total volume of them, V, is V_f + V_g, where V_f is volume occupied by saturated liquid while V_g is volume occupied by saturated vapor.

    x= m_f/m_total

    V= mv ---> m_total v_avg= m_f*v_f + m_g*v_g
    also, we know
    m_f= m_total- m_g ---> m_total* v_avg = (m_total-m_g)v_f+ m_g*v_g
    dividing by m_total, we have
    v_avg= (1-x) v_f + xv_g

    and since x= m_f/m_total, we rewrite the equation...
    v_avg= v_f + xv_fg
    where v_fg= v_g - v_f and the subscript "avg" is usually dropped for simplicity.

    The book says these analysis can be repeated for internal energy, u and enthalpy, h....Could anybody tell me how?

  2. jcsd
  3. Mar 24, 2015 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Have you tried substituting hf and hfg for vf and vfg in the derivation of vavg?

    You don't have to re-invent the wheel, mathematically speaking, each time you want to calculate the average of a certain physical property.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook