3. Consider a fluid obeying the equation of state: p=a74, where a is a constant. The specific heat at constant volume is also given to you: CV=12pV/T. a.) Calculate the internal energy U(p,V) for this fluid. You may assume that the internal energy per mole of the fluid is a function of temperature only. b.) Calculate the pressure as a function of volume, p(V), as the fluid undergoes a adiabatic transformation. c.) Plot the closed curve in the pV plane for a Carnot cycle using this fluid. d.) Now, derive explicitly the efficiency of a Carnot engine using this fluid. (We can indeed change the working substance of the Carnot engine at will. We don't always have to use the ideal gas!)