1. The Carnot cycle uses an ideal gas that completes a cycle by going under adiabatic and isothermal processes. (a) Find the amount of work that will be done in this cycle. Present your solution thoroughly by showing the graph at each step, the amount of work and heat for each step and the net work that you will find. (b) If the efficiency of this cycle is calculated as the amount of work that you get to the amount of energy (heat) that is paid, derive the equation of efficiency in terms of heat of cold and hot reservoir. Is there also a way to represent efficiency in terms of temperatures of hot and cold reservoir? (c) From your answers to parts (a) and (b) explain thoroughly why you can’t have a heat engine with 100% efficiency?