Question

A 4.50-kg block of ice at 0.00∘C falls into the ocean and melts. The average temperature of the ocean is 3.50∘C, including all the deep water. By how much does the change of this ice to water at 3.50∘C alter the entropy of the world? (Hint: Do you think that the ocean temperature will change appreciably as the ice melts?) Does the entropy increase or decrease?

Answer 1

Solution:

Given, mass of ice = 4.5 kg = 4500 grams

Here, heat transferred to ice = heat to melt + heat to increase temp to 3.5^oC = (4500)(333) + (4500)(4.184)(3.50) = 1564398 J

Change in entropy of the ocean = heat lost / temp = -1564398 / (273.15 + 3.5) = -5657.9 J/K

Change in entropy for ice = ( mL / T) + m c ln(T_final / T_initial) = {(4500 x 333) / 273 } + 4500 x 4.184 x ln (276.5/273) = 5728.9 J/K

Total change in entropy = ocean + ice = - 5657.9 + 5728.9 = +71 J/K