(Solved): QUESTION 3 (The Carnot engine) A reversible heat engine receives heat from a reservoir which is ...

QUESTION 3 (The Carnot engine) A reversible heat engine receives heat from a reservoir which is at a temperature of $600^{?}\mathrm{C}$ and then rejects it to another at $0^{?}\mathrm{C}$. The heat supplied is $2000\mathrm{kJ}$. Determine the following: 3.1. The thermal efficiency of the engine. 3.2. The work produced by the engine. 3.3. The heat rejected. [9] QUESTION 4 (Thermodynamic relationships) A tank of a water heater has $V=0.1{\mathrm{m}}^3$ and is initially sealed and full of water at $T=$ $328\mathrm{K}$ and $P=0.1\mathrm{MPa}$. The water heater is designed to maintain the water at this temperature, but due to a fault in the temperature sensor, the heating element comes on and remains on. The temperature of the water increases, but there is no space into 2 which the water can expand. The tank has a pressure relief value that is designed to open at $P=1\mathrm{MPa}$. At what water temperature will this occur? Assume the isothermal compressibility and coefficient of thermal expansion of water are constant at ${?}_V=2.90\times 10^{?4}{\mathrm{K}}^{?1}$ and $K_T=4.50\times 10^{?10}{\mathrm{Pa}}^{?1}$ [5]