1) Adiabatic and isothermal compressions and expansions of an ideal gas. An ideal gas is the simplest system through one can understand adiabatic and isothermal changes of state because the calculations can be done analytically. In this problem I will lead you through a series of adiabatic and isothermal changes that return the gas to its initial state. Note that once the gas is returned to its initial state, all of the state variables of the gas are the same as when they started, (e.g. T, P, U, V, H, etc.). But going through this cycle we are able to input heat from a hot temperature bath and output both heat to a cold temperature bath and work (in this case PV work) to the surroundings. a) Isothermal Expansion: The gas is brought into contact with a heat bath at TH=T0= 500K and is isothermally expanded until P1=3 bar. b) Adiabatic Expansion: The gas is decoupled from the bath and expanded adiabatically until P2=2 bar. c) Isothermal Compression: The gas is brought into contact with a heat bath at TC= T2 and is isothermally compressed until P3=2.66bar. d) Adiabatic Compression: The gas is decoupled from the bath and compressed adiabatically until P4=P0=4 bar. Sample table: Note: For P,T, and V give the value after each step. For U,S,Q, and W give the value during the step (they are differences). For the total, only need to sum the last 4 columns. You have a steam turbine that is supplied steam at a rate of 1kg/sec at a T and P of 600C and 15MPa. The pressure on the downstream side of the turbine is 0.5MPa. What is the minimum temperature on the downstream side of the turbine if it acts adiabatically? What is the maximum work out