100 g of water at 80 degC is mixed adiabatically with 100 g of water at 20 degC (specific heat 4.18 J g^-1K^-1, constant). The entropy change of the universe is closest to

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$100 g$ of water at $8 0^{\circ} C$ is mixed adiabatically with $100 g$ of water at $2 0^{\circ} C$ (specific heat $4.18 J g^{- 1} K^{- 1}$ , constant). The entropy change of the universe is closest to

Final temperature

= 5 0^{\circ} C = 323.15 K

Δ S = m c [ln (323.15/353.15) + ln (323.15/293.15)] = 418 [- 0.0888 + 0.0974] = + 3.62 J K^{- 1}

. The system is isolated so this is

Δ S_{u ni v}

, positive for an irreversible mixing. Using Celsius values inside the logarithms gives a different, wrong number.