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Entropy change of the universe

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5.9 Two equal quantities of water, of mass m and at temperatures T1, and T2, are adiabatically mixed together, the pressure remaining constant. Show that the entropy change of the universe is
[see the attachment for the equation]
where c_p, is the specific heat of water at constant pressure. Show that [delta]S >= 0. (Hint: (a - b)^2 0 for a and b real.)

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We calculate the entropy change of the universe involved in adiabatically mixing two equal quantities of water, initially at different temperatures.

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