A simple engine uses an ideal gas with constant specific heats as the working fluid in a closed, piston-cylinder system. The gas is first heated at constant pressure from state 1 to state 2, then cooled at constant volume to state 3, where T3 = T1, and then compressed at constant temperature, thereby returning to state 1. Derive expressions for the work and heat transfer per unit mass of gas for each process in terms of the temperatures and pressures at each state and the thermodynamic properties cp, cv, and R.