Question 1: Entropy

a) In a coal fired thermal power station, indicate where the exergy contained in the coal is destroyed. For each exergy destruction mechanism, explain whether there is a small or large exergy destruction occurring.                                 

b) An inventor proposes a thermal power cycle to power a ship based on the heat contained in sea water around the ship. How might electricity be generated from this heat source? (i.e. what kind of conversion cycle could one use?). Make reasonable assumptions to explain whether you think this idea is feasible. Explain your answer.           

Question 2: Exergy

An inventor proposes a vehicle driven by a compressed air motor. The source of compressed air is a tank of volume 0.8m³ and with maximum pressure of 20 MPa. The tank is initially at room temperature, 20ºC. Assume that the air has constant heat capacity c_p=1.0 kJkg^-1K^-1 and c_v=0.716 kJkg^-1K^-1.

a) If the tank is heated to 60ºC, calculate the pressure in the tank.                              

b) Calculate the amount of heat required to heat the air in the tank to 60ºC.

c) Calculate the maximum work that can be extracted from the compressed air by an ideal reversible process.                        

d) Comment on the usefulness of the idea for vehicle propulsion.

Question 3 Cycles

A thermodynamic gas cycle consists of four (quasi-equilibrium) processes:

Process 1->2 Adiabatic compression

Process 2->3 Isobaric heating

Process 3->4 Isothermal expansion

Process 4->1 Isochoric cooling

a) Draw a pressure-volume diagram for this cycle                                         

b) Draw a temperature-entropy diagram for this cycle                                               

c) Draw a pressure-enthalpy diagram for this cycle                                        

Question 4 Otto Cycle

Consider an air standard Otto cycle with compression ratio of 8 and a swept volume of 300 cc (i.e v₂-v₁=0.3 L). At the start of the compression process, the pressure is 90 kPa and the temperature is 300 K. Also, c_p/c_v=1.4

a)  Calculate the cylinder pressure at the end of the compression process.  

b)  Heat is input by internal combustion of fuel. Assuming that the air to fuel mass ratio is 12:1 and the specific energy content of the fuel is 25 MJ/kg, calculate the temperature and pressure at the end of an ideal constant volume heating process. Assume that the heat capacity of the working fluid and combustion products are both given by c_v=0.718 kJ/kgK.                       c)  Briefly explain what limits the compression ratio in real Otto cycle (petrol) engines and why the same limitation does not apply to Diesel cycle engines.   

d) Explain how the four processes in a real engine depart from the ideal Otto cycle.

Question 5 Rankine Cycle

An ideal Rankine cycle using water as the working fluid operates at a maximum boiler pressure of 3 MPa and fixed condensing temperature of 40ºC.

b)  If the quality of steam at the turbine outlet must remain above 85% to avoid damage to the turbine blades, calculate the maximum cycle thermal efficiency.                     

c) Sketch, on the same plot, a comparison of the ideal Rankine cycle with a real Rankine cycle operating under the same conditions. Numerical calculations are not required.                                                                                                                                    

d) List three methods of increasing the efficiency or work output of a Rankine cycle and explain how the method improves the cycle in each case.