Massachusetts Institute of Technology DEPARTMENT OF MECHANICAL ENGINEERING Center for Ocean Engineering 2 611 SHIP POWER and PROPULSION Problem Set 4 Basic Thermodynamic Cycles Due November 2 2006 1 First Law refreshera Write the generic first law thermodynamic equation for a single inlet and single exit flow b What does this equation not take into account c Discuss the adiabatic process the polytropic process and what it means for a process to be reversible 2 Air at 10 C and 80kPa enters the diffuser of a jet engine steadily with a velocity of 200 m s The inlet area of the diffuser is 0 5 m2 The air leaves the diffuser with a velocity that is very small compared with the inlet velocity Assume the diffuser is the system flow is steady and air is an ideal gas R 287 kPA m3 kg K enthalpy 283 Kelvin 283 kJ kg Determine a The mass flow rate of the air b The temperature of the air leaving the diffuser 3 Consider the tank system below Tank A has a volume of 100ft3 and initially contains R134a at a pressure of 100 kPa and a temperature of 313 Kelvin The compressor evacuates tank A and charges tank B Tank B is initially evacuated and is of such volume that the final pressure of the R134a in tank B is 800 kPa Temperature remains constant Determine the work done by the compressor 4 Steam enters an adiabatic turbine at 8 MPa and 500C with a mass flow rate of 3kg s and leaves at 30 kPa The isentropic efficiency of the turbine is 9 Neglecting kinetic energy determine a Temperature at the turbine exit b Power output 5 A marine steam plant operates as a simple Rankine cycle with a turbine inlet temperature and pressure of 600 C and 4 MPa The condenser operates at a pressure of 20kPa Assume that the turbine isentropic efficiency is 80 and the pump isentropic efficiency is 90 a Sketch the cycle on T s and h s diagrams b Determine the steam quality at exit from the turbine c Determine the specific enthalpy change across each component d Determine the net power of the cycle with a mass flow rate of 3 kg s e Determine the thermal efficiency of the Rankine cycle