 Entropy generation by mixing equal thermal masses

ID: entropy-generation-by-mixing-equal-thermal-masses

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

M c_{P} ln (T_{f} / T_{1}) + M c_{P} ln (T_{f} / T_{2}) = 2 M c_{P} ln [(T_{1} + T_{2}) / (2 T_{1} T_{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.

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