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 refresher- a) 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 10º 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 output5. 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