1(a) 1kg of water at a temperature of 20°C is placed in contact with a cold reservoir held at a constant temperature of 4°C. (i) What is the change in the internal energy of the water as it cools to 4°C ?(The specific heat capacity of water is 4148 J K-¹ kg¯¹.) (ii) Calculate the change in entropy of the water as it cools to 4°C. (iii) Calculate the change in entropy of the cold reservoir. (iv) Is this process of cooling the water reversible or irreversible? Explain your answer. Assume now that rather than being placed in a direct contact with the cold reservoir the water is cooled from 20°C to 4°C by using the water as the heat source for a reversible heat engine. The cold reservoir still has a fixed temperature of 4°C. How much work can be extracted from this heat engine? (b) A heat engine uses the cycle shown below where AB is an isobaric process, BC is isochoric and CA is adiabatic.

The system is an ideal gas. Show that the efficiency of the cycle, n, is given by \eta=1-\frac{\left(\frac{T_{A}}{T_{C}}\right)^{\frac{1-\gamma}{1-1}}-1}{\gamma\left(\left(\frac{T_{C}}{T_{A}}\right)^{\frac{1}{\gamma-1}}-1\right)} where TA and Te are the temperatures of the gas at points A and C, and is the adiabatic index of the gas.