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38. 100g of water is contained in a 200 g aluminum vessel at 20 °C. (a) If an additional 50 g of water at 100 °C is poured into the container, what is the final equilibrium temperature of the system? (b) How much ice at -20 °C must you now add to the system, such that the final tempera- ture will be 0°C with only water remaining in the container?

Answer 1

@ Speulic heat of aluminium 15 CA=og Galorie Igie (A=0-215 callgmoc a when sog of hot water is paned its heat transfernes to aluminium vessel of water already Present. • Let the final temperature be T°C. The heat given by water is H, = mcot Hi = SOXIX (100-1) Calul . Since specific heat of water = 16/8% heat aborbed by wath & aluminium is Hy=100 XI X (T-20) + 200 x 0.215 XC 7-20) Cat (2) - but Hi=H2 · Soe 100-T) - 100 (T-20) +200 X0-215C7-20) 9100-T = 27-40 + 4X0.215 CT-20) 9100-T= 27-40 +0.86T -34.4 100 +40+34.4 = 2T+0·86 T + :: 3.867 = 174.4 T-174.4 °C 3086 545.200 T= 45.2°C 6 Heat given by ice is absorbed by ice - H=H, H2 where Hi - mcot while Hy is due to latent heat H = mxoug2o + mx 80 calorie f :. mxo'ng (20+mX80 = (100+50) X1 X45:2 + 200 X 0.215 x 45.2 &m (80+ 9.8) = 67.80 + 1943:6 im = 872.350 597.19 8723.6 m = m=9718