Find entropy change of total system of heatbath + water when water is placed in heat bath from 20 C to 50 C, then 50C to 80C. assume equilibrium is reached first in both cases.
water = 1000g , C = 4.2J/C/G
The Attempt at a Solution
the entropy for water Sw = CdT / T + Cdt / T , where first integral from 293K to 323K, second from 323K to 353K.
bath entropy Sb = -C(353 - 293) / 353
S-total = 66.6 J/K
but ans is 35.6J/K .
apparently, the 2 step process of heating should get me a smaller entropy change, but the value i calculated 66.6 is around the same as if i did a 1 step heating from 20 to 80 straight.
so where did i go wrong? thanks!