Final answer:
When 1 kg of ice at 0°C melts to water at 0°C, the entropy increases due to the heat absorbed during the phase change, and the change in entropy is 1.22×103 J/K.
Step-by-step explanation:
When 1 kg of ice at 0°C melts to water at the same temperature, the entropy of the system increases. The latent heat of fusion for ice is given as 80 cal/g, but we will use the value with SI units, which is 334 kJ/kg. The formula to calculate the change in entropy (ΔS) during the melting process is: ΔS = Q / T. where Q is the heat absorbed by the ice to melt, and T is the absolute temperature in Kelvin. First, we need to convert the latent heat to Joules using the given value: Q = (1 kg)(334 kJ/kg) = 334 kJ = 334×103 J. The melting temperature of the ice in Kelvin is T = 0°C + 273.15 = 273.15 K. Substituting these values into the formula gives us the increase in entropy: ΔS = 334×103 J / 273.15 K. After calculating, we will obtain: ΔS = 1.22×103 J/K. Therefore, when 1 kg of ice at 0°C melts to water at 0°C, the change in entropy is 1.22×103 J/K.