Problem 1 (25 p): a) How many processes occurs in Carnot's cycle? Sketch all the processes. b) Sketch the P-v diagram of Carnot's cycle. c) Derive the equation for the Carnot's heat efficiency d) Describe the Carnot's principles Problem 2 (25 p): For gases, the relationship between the specific heat at constant pressure and constant volume is given by; Cp = Cy + R. Derive this relationship by using the ideal gas equation. Fill the table shown below. Comment on the - ratio for number of atoms in a gas molecule. Use for the table: Ah = CpAT, Au = CAT Approximation of Temperature-Independent Heat Capacities of an Ideal Gas Mono-atomic gases Two-atomic gases Three-atomic gases Degree of freedom DOF DOF = 3 DOF = 5 DOF = 6 Heat capacity at DOF constant volume CD = R 2 Heat capacity at constant pressure Adiabatic exponent index k = Cp Cy Specific Internal Energy Specific EnthalpyProblem 1 (25 p): 4 kg of water at 25 C and 0.3 M Pa is heated in a sealed tank under constant pressure. 10000 kJ of heat is added, what is the change in the entropy? Problem 2 (25 p): Carnot's cycle for a heat engine that works with air is given in Figure 1. TH = 300 C, T1 = 150 C, qH = 169kJ/kg and PA = 65 kPa. Determine v1, P1, and Wnet. R = 0.287 kJ kg. k' -qL = RTLIn (12 )