Chapter 3 Formula Sheet

Formula Units
Quality

    \[x=\frac{m_{vapor}}{m_{total}}(vapour \ mass \ fraction)\]

    \[1-x=\frac{m_{liquid}}{m_{total}}(liquid \ mass \ fraction)\]

Specific Volume

    \[v=v_f+xv_{fg}\]

    \[m^3/kg\]

Specific Internal Energy

    \[u=u_f+xu_{fg}\]

Specific Enthalpy

    \[h=h_f+xh_{fg}\]

Specific Heat Ratio

    \[K=\frac{C_p}{C_v}\]

Ideal-Gas Law

    \[P<<P_c\]

    \[T<<T_c\]

    \[z=1\]

  • Equations
  •     \[Pv=RT\]

        \[Pv=mRT=n\bar{R}T\]

  • Gas Constant
  •     \[R=\frac{R}{M}\]

        \[M=mulecule \ mass\]

        \[kJ/kg K\]

    Compressibility Factor Z

        \[Pv=ZRT\]

        \[Z=\frac{P\bar{v}}{\bar{R}T}\]

    Reduced Properties

        \[P_R=\frac{P}{P_c}\]

        \[T_R=\frac{T}{T_c}\]

    Pseudo-Specific Volume

        \[v'_R=\frac{vP_c}{RT_c}\]

    Constants Units
    Universal Gas Constant

        \[\bar{R}=8.314\]

        \[kJ/kmol\times K\]

    Molecular Weight of Air

        \[M_{air}=28.97\]

        \[Kg/kmol\]

    Critical Temperature for Air

        \[T_c=133\]

        \[K\]

    Critical Pressure for Air

        \[P_c=37.7\]

        \[bar\]