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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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Calculating entropy of water, reservoirs, and universe

I need some help with this problem. Here is the problem. Btw, this is problem #5.4 from Equilibrium Thermodynamics 3rd edition by C.J. Adkins

1*10^-3 m^3 of water is warmed from 20 to 100 degrees Celsius A) by placing it in contact with a large reservoir at 100 degrees Celsius, B) by placing it first in contact with a large reservoir at 50 degrees Celsius until it reaches that temperature, and then in contact with the reservoir at 100 degrees Celsius, and C) by operating a reversible heat engine between it and the reservoir at 100 degrees Celsius. In each case, what are the entropy changes of 1) the water 2) the reservoirs, and 3) the universe?

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