Thermodynamics: h vs u and Quality?

  1. Hi,

    I am trying to understand the solution to a quiz I had, and am having trouble.

    The question was:
    The solution says:
    First off, why (when they solve for internal energy and specific volume) do thy use the formula (Quality)*Uvapor + (1-quality)*Uliquid ? This makes sense to me in my head, but it says no our text that the generic equation for u,h,or v is:
    Y = Yliq + (Quality)*Ysat.vapor

    so why dont they use it in this scenario?

    Second, why do they use internal energy and not enthalpy?


    --a lost Mechanical engineering student
  2. jcsd
  3. Q_Goest

    Q_Goest 2,989
    Science Advisor
    Homework Helper
    Gold Member

    The equation you're trying to write: Y = Yliq + (Quality)*Ysat.vapor

    ... is off just a bit. The correct equation is: Y = Yf + X Yfg
    Where Yf is the fluid property at 100% saturated liquid
    Yfg is the difference between the fluid property at 100% saturated gas and 100% saturated liquid.

    Regarding why not enthalpy, if you rewrite the first law it helps to clear this up. Normally, we write:
    dU = dQ + dW

    But for any control volume with flow in and out, we can also rewrite it:
    dU = dQ + dW + dH
    dH = (Uin + pVin) - (Uout + pVout)
    Note that gas flowing into or out of a control volume does work pV so we say H = U + pV
    (See ref: )

    So if we apply this to the system with two separated tanks that has a control surface around both tanks, we find no heat or work crossing the control surface (dQ=0 and dW=0), nor do we find any flow across the control surface, so dH = 0. All we're left with is dU = 0 (or U1 + U2 = U3).
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