= Liquefaction yield with separate warm-gas and liquid outlets
{title2=$y=(h_g-h_{\rm in}-q)/(h_g-h_l)$}
Apply the <steady-flow energy balance> to an entire <liquefaction> apparatus, allowing a warm <gas> outlet and a separate cold <liquid> outlet. With incoming <heat> $q$ per unit feed <mass>, no shaft <work>, and negligible changes in bulk <kinetic energy> and gravitational <potential energy>, <conservation of mass> and <conservation of energy> give $h_{\rm in}+q=yh_l+(1-y)h_g$. Solving this equation gives the displayed liquid <mass fraction>.
The two outlet streams need not share a <temperature>. For example, a <counterflow heat exchanger> can warm returning <gas> before it crosses the overall <control volume> boundary, while collected <liquid> leaves at the cold end. When the outlet temperatures differ, $h_g-h_l$ includes sensible heating as well as phase change; it is not simply a <latent heat>. A colder two-phase separator nested inside the apparatus has its own boundary states and a different local enthalpy balance.
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