A mole of a. monatomic ideal gas with pressure, P1. and volume, V , is freely and adiabati cally expanded to V2 (free expansion is dened as expansion into zero pressure). It is then quasistatically compressed to a volume V1 while maintaining the pressure at P2 [isobaric process). Finally. the gas is heated quasistatically until the pressure returns to P1 while the volume remains V]. This cycle is called Mayer's cycle. (a) [5 points) 1What is the internal energyr of the system after the rst step of free expansion? (b) [5 points) Sketch this process on a P V diagram. clearly indicating which steps of the process are quasistatic with a solid line and not quasistatic with a dashed line. State the relationship between P and V for the free expansion step. (c) [10 points) Calculate the work and heat transfers at each step of the cycle, and verify that the overall internal energy change of the gas is zero over the entire cycle. (d) [10 points) Using the computed work and heat transfers of the cycle, derive a relation between the Ca and CL. for an ideal gas. assuming constant heat capacities. (e) [ll] points) Find the entropy change of the gas that occurred in the free expansion step