A 1.00 kg ice cube, initially at 0 °C, is placed in a container of liquid water. The liquid water has a mass of 3.00 kg and an initial temperature of 27.5 °C. After some time, the ice completely melts into the water and thermal equilibrium is reached. Assume that the ice and liquid water are completely insulated from the environment during this process. The latent heat of fusion of water is 3.335×10^5 J kg^−1, and the specific heat of liquid water is 4186 J kg^−1 K^−1.
(a) Calculate the final temperature of the system when thermal equilibrium is reached. Give your answer in degrees Celsius (°C).
(b) Calculate the total entropy change of the original liquid water during this process. Start with ΔS = ∫ dQ/T and carry out the integral. Show all work for full credit. Give your answer in units of Joules per Kelvin (J/K).
(c) Calculate the total entropy change of the ice cube during this process, in J/K. Start with ΔS = ∫ dQ/T and carry out the integral. Show all work for full credit.
(d) What is the total entropy change of the universe as a result of this process, in J/K? Based on your answer, is the process reversible or irreversible?