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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?

Thanks.

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

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