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i) What is the efficiency of a Carnot engine operating between a high temperature reservoir at 100∘C and a low temperature reservoir at 10∘C ? ii) What is the work done in one hour by a Carnot engine operating between a high temperature reservoir at 100∘C and a low temperature reservoir at 10∘C ? The heat flow from the high temperature reservoir is 400 J/s. (b) (7 marks) A 0.20 kg block of copper is heated in a laboratory oven to a temperature of 180∘C. It is added to an insulated container of ice and water. The mass of ice is 0.10 kg and the mass of water is 0.90 kg, and both water and ice are at a temperature of 0∘C. i) Calculate the heat required to melt all the ice in the container. ii) Calculate the heat released if the 0.20 kg block of copper is cooled from 180∘C to 0∘C. iii) Find the final temperature of the contents of the container. Neglect the heat capacity of the container. Assume no heat is lost to the surroundings. The specific heat capacity of copper is 381 J kg−1 K−1 The specific heat capacity of liquid water is 4.19 kJ kg−1 K−1 The latent heat of fusion of water is 333 kJ kg−1 The latent heat of vaporisation of water is 2260 kJ kg−1 (c) (7 marks) A steel rod is 3.000 cm in diameter at 25.00∘C. A brass ring has an interior diameter of 2.992 cm at 25.00∘C. Find the common temperature at which the steel rod just fits inside the brass ring. The coefficient of linear expansion of steel is 11×10−6/∘C The coefficient of linear expansion of brass is 19×10−6/∘C