= Entropy generation by mixing equal thermal masses
{title2=$\Delta S=2Mc_P\ln\frac{T_1+T_2}{2\sqrt{T_1T_2}}$}
For equal <masses> $M$ of the same liquid with constant specific heat $c_P$, adiabatic constant-pressure mixing gives final <temperature> $T_f=(T_1+T_2)/2$ by <enthalpy> conservation. The <entropy> change is $Mc_P\ln(T_f/T_1)+Mc_P\ln(T_f/T_2)=2Mc_P\ln[(T_1+T_2)/(2\sqrt{T_1T_2})]$. The <arithmetic-geometric mean inequality> proves nonnegativity, with equality only for equal initial <temperatures>. There is no separate compositional mixing <entropy> for identical fluids.
Back to article page
