First Exam of CheE Thermodynamics 10/12/2017 1. A Joule-Thomson expansion device is used as releasing valve. The inlet waste gas is at temperature of 300oC and pressure of 3000 kPa, and the waste gas is released to the atmosphere (i.e., the pressure is at 100 kPa). Please calculate the releasing temperature at the outlet. Assume that (a) the gas is a steam; (b) the gas is not an ideal gas and the equation of state is (P+a/V2)(V – b)=RT where a is negligibly small and b= 3 m3/mol x 105. The constant-pressure heat capacity of the gas is 30 J/mol K. Noted that the process is an adiabatic and reversible process and no shaft work involved. (20 %) 2. A air tank is at temperature 600K and pressure of 40 bar in the beginning. Please calculate the final temperature if (a) the air is just released to the atmosphere; (b) the air is repressurized to 80 bar by an inlet air at 600K and 100 bar; (c) the air is released to another tank having twice the volume of the air tank and it is empty in the beginning. Assume the process is carried out adiabatically and reversibly and the air can be treated as ideal gas. Known that the constant-pressure heat capacity of the gas is 30 J/mol K. (20 %) 3. Assuming that the working fluid is an ideal gas with Cp=a (constant), draw PressureVolume diagram (i.e., P versus V plot) and Temperature-Entropy diagram (i.e., T versus S plot) for each of following cycles and develop expressions for their maximum thermodynamic efficiency, . (20 %) (a). Carnot Cycle Engine (1) Isothermal expansion, (2) Reversible adiabatic expansion, (3) Isothermal compression, (4) Reversible adiabatic compression. (b). Stirling Cycle Engine (1) Isothermal expansion, (2) Constant volume cooling. (3) Isothermal compression, (4) Constant volume heating. 4. Derive the following relations for real substance and please start your derivation from dU = dQ - PdV. dH = Cp/T dT + [ ]dP (5 %) 5. Derive the following state variables and thermodynamic properties through Gibbs free energy, G(T, P) (a). S(T, P); (b) U(T, P); (c) A(T, P); (d) Cp(T, P) (10 %) 6. Please prove that DG < 0 for a spontaneous process. (5 %) 7. (a) A gas turbine in a small electric power plant is designed to accept A kg/hr of gas at P1 bar and T1 K and exhaust the gas at P3 bar. Assuming that the gas turbine is adiabatic and has been well designed (so that the entropy generation rate ~ 0), please compute the exit temperature and the power generated by the turbine. (b) The efficiency of a turbine is defined to be the ratio of the work actually obtained if the turbine operated isentropically between the same inlet and exit pressure. If the turbine in part (a) is adiabatic but only 80 percent efficient, what would be the exit temperature of the steam? (20 %) Assume the gas is an ideal gas and the constant-pressure heat capacity is Cp*=a