Expansion

GT

First Law of Thermodynamics: ${\dot{w}}_{turb}=h_3-h_4>0$
Second Law of Thermodynamics: $s_3=s_4$

Free Expansion

First Law of Thermodynamics: $h_3=h_4$ ($\dot{w}=0$)
Second Law of Thermodynamics: $s_4>s_3$