# Example - FAMU-FSU Eng College Example 1 The internal energy of a closed system can be increased by adding heat or doing work. In the following example, 1 kg of saturated liquid water at 100C is contained inside a piston-cylinder assembly. Instead of adding heat, a paddle wheel is doing work on the system and the water is undergoing a transition into 100% saturated vapor. During the process the piston moves freely inside the cylinder. Question: Does this make a difference in our calculation? Assume no heat transfer, determine the work done and the amount of entropy production. U=Q-W=0-W=-W m(ug-uf)=-W, ug: saturated vapor, uf: saturated liquid W=- (ug-uf)=-(2506.5-418.9)=-2087.6(kJ/kg) from Table A-4 Q Entropy change : s s generation , s s generation T since there is no heat transfer (s)gen=sg-sf=7.356-1.307=6.049 (kJ/kg K), from Table A-4 Answer: Yes, if the piston is fixed, the pressure inside the cylinder will increase as the liquid evaporates into vapor. Accordingly, the saturation state will change. Example 2 Steam enters a turbine with a pressure of 3 MPa, a temp. of 400C, and a velocity of 150 m/s. 100% saturated vapor exits at 100C with a velocity of 50 m/s. At steady state, the turbine develops work of 500 kJ per kg of steam. There is heat transfer between the turbine and its surroundings at an averaged surface temperature of 500 K. Determine the rate at which entropy is produced within the

turbine per kg of steam. 1 T 1 dW/dt 2 dQ/dt at 500 K 2 s Solution- Example 2 dm Mass conservation : 0 m 1 m 2 , m m 1 m 2 dt ds Q Entropy balance analysis : m 1s1 m 2 s2 s generation dt T ds Q Steady state : 0 m 1s1 m 2 s2 s gen dt T 1 1 Q

, s , and s sgen ( s2 s1 ), Need to determine Q 2 1 m m T b From table A - 4, saturated table, s2 sg 7.356( kJ / kgK ) From table A - 6, superheate d table, s1 6.922(kJ / kgK ) ? Question : How do we determine Q Solution- Example 2 Use Energy balance equation of course : dE dE g dW dE dE g Q E1 E2 , 0 dt dt dt dt dt 2 2

V V dW Q m 1 (h1 1 ) m 2 (h2 2 ) 2 2 dt Q 1 1 dW h1 h2 V12 V22 m 2 m dt Table A - 6, superheated vapor, h1 3230.8( kJ / kg ) Table A - 4, saturated table, h 2 hg 2676(kJ / kg ) Q 1 (3230.8 2676) (1502 502 )(1 / 1000) 500 64.8( kJ / kg ) m 2 1 1 Q From previous page : sgen ( s2 s1 ) m m Tb 64.8 (7.356 6.922) 0.564( kJ / kg K ) 500