(a) (i) State the first law of thermodynamics. (ii) Write the mathematical expression for the first law of thermodynamics and identify each term. [4 marks] (b) A Carnot engine operates between a source temperature of 627°C and a sink temperature of 27°C. (i) Calculate the efficiency of the engine. (ii) If the engine absorbs 5000 J of heat from the source in each cycle, calculate: (I) the work done by the engine per cycle. (II) the heat rejected to the sink per cycle. [8 marks] (c) (i) Explain why the efficiency of a Carnot engine is always less than 100% in practice. (ii) State ONE way in which the efficiency of a heat engine can be increased. [4 marks]