Energy conservation law => heat lost by the hot water = heat gained by ice
At the equilibrium the temperature of mixture is T.
heat lost by the hot water mCsΔT = 75.3g * 1 cal /(g°C) *(55.3°C - T)
heat gained by the ice = latent fusion heat at 0°C + heat absorbed to rise temperature from 0°C to the equilibrium temperature of the mixture, T
latent fusion heat of ice per gram, at 0°C = 79.7 cal/g
latent fusion heat of ice at 0°C = 21.4g *79.7 cal/g
Heat absorbed to rise the temperature until thermal equilibrium:mCsΔT = 21.4g*1cal(g°C)*(T-0°C)
Total heat gained by ice = total heat lost by the hot water
21.4g * 79.7 cal/g + 21.4g*1cal/(g°C)*(T) = 75.3g * 1 cal /(g°C) *(55.3°C - T)
1705.58 + 21.4 T = 4164.09 - 75.3T
21.4T + 75.3T = 4164.09 - 1705.58
96.7T = 2458.51
T = 2458.51 / 96.7
T = 25.42 °C
Answer: 25.4 °C
