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Unformatted text preview: MECH 310 Thermodynamics I January 22, 2007 American University of Beirut, Fall 2007 Handout # Final Exam Final Exam • This is a 180 minutes exam. • You are allowed to bring in 3 cheat sheets in addition to the thermodynamic tables. • You are advised to read the whole exam before you start. • Make sure you state all the assumptions you make and that you clearly identify any control mass or control volume you utilize in your analysis. • Good luck! Name : Section : Solve 5 of the following 6 problems. Make sure your choice is clear. 1 Problem 1 [20 points] One ton of water is in a fixedvolume container. Initially, the temperature is T 1 = 190 ◦ C and the pressure is p 1 = 10 bar. It is desired to raise the pressure to p 2 = 30 bar. This is achieved by interactions with another system that transfer energy and 1000 kJ/K of entropy into the container. (a) How much energy is transferred? (b) How entropy is generated by irreversibility? (c) What are the possible types of interactions that could result in the given transfers of energy and entropy? correction: [control mass : 2 pts] [state 1: 2 pts], [state 2: 3 pts], [energy: 5 pts], [ir rversibility : 5 pts], [part (c): 3 pts]. Problem 1 Solution (a) Take the container as the control mass. Initial state is p 1 = 10 bar T 1 = 190 ◦ C s 1 = 6 . 641 kJ/kg.K v 1 = 0 . 2002 m 3 /kg u 1 = 2603 kJ/kg Since the container is closed, the specific volume remains unchanged, so that the final state is given p 2 = 30 bar v 2 = 0 . 2002 m 3 /kg T 2 = 1030 ◦ C s 2 = 8 . 461 kJ/kg.K u 2 = 4108 . 1 kJ/kg Applying the first law for a control mass, the energy transferred into the container is W ← + Q ← = U 2 U 1 = m ( u 2 u 1 ) = 1000(4108 . 1 2603) = 1505100 kJ (b) Applying the second law for a control mass, Δ S = S ← + S irr ⇒ S irr = m ( s 2 s 1 ) S ← = 1000(8 . 461 6 . 641) 1000 = 820 kJ/K (c) The energy transferred into the container has to be heat since it is the only way to transport entropy across the boundary of a closed system. 2 Problem 2 [20 points] Consider a gas turbine consisting of a compressor, combustion chamber and a turbine as shown in the figure below. The compressor and turbine are coupled by a common shaft as shown in the figure. If the net work of the cycle is zero meaning that the work produced by the turbine is equal to the work consumed by the compressor, find the pressure of the air...
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