An ideal gas is contained within a piston-cylinder arrangement and undergoes a Stirling Cycle, which consists of four separate thermodynamic processes:
Isothermal Compression: From state 1 to state 2 along a pV = constant process.
Isometric Process: From state 2 to state 3 during which the temperature of the gas increases.
Isothermal Expansion: From state 3 to state 4 along a pV = constant process.
Isometric Process: From state 4 to state 1 during which the temperature of the gas drops. Neglecting changes in the kinetic and potential energy of the gas,
(a) derive an expression for the net work transfer for the cycle. Prove that for a Stirling Cycle, the net work transfer is always from the system to the surroundings. Hint: Do not attempt to put numbers in.
(b) Prove that there must be a net transfer of heat from the surroundings in order for the system to deliver work.
(c) Find the net work transfer for the cycle if 1 bar 1 p = , 4 bar 2 p = , 20 bar 3 p = , 5 bar 4 p = and 3 2v2 = 3m^3 .
(d) For the data supplied in part (c), use Excel to accurately plot the cycle on a pressure vs volume diagram (make sure the chart is fully labelled and proper units have been used). Import the Excel Chart into the main text of your Word document. For the two isothermal processes, fit an appropriate curve to each process and display the equation of this curve on the Excel Chart.