Question

Pressurized air stored in a 10,000 m2 cavern at 500 kPa and 400K is to be used to drive a turbine at times of high demand for electric power. If the turbine exit conditions are 100 kPa and 300 K, determine the amount of work delivered by the turbine when the air pressure in the cave drops to 300 kPa. Assume both the cavern and the turbine to be adiabatic and that the rate of discharge of the cave is sufficiently slow that the turbine may be considered to operate in a quasi-steady fashion. 100 kPa 300 K Shaft Work Turbine 10,000 m Cavern

Answer 1

Given: Volume of caverna Vs 10,000 m3 considering turbine e cavern combined as control volume shown. Pe: 100kPa , Tes 300k P = Sook Pa, Ti - 400C. P, - Зоо 1 PG I to find I work delivered by turbine.(W): to, boom Soska HT=400% --- Apply unsteady flow energy equation to the control volume shown: de cv = mihi-niebe + Giv - weol o de nye EC sraute of Now, the mass accumulation rate equation of control Forume gives: micv: mi-mie I but mizo Tmere - ne] (2) change of inner energy. of control VoIMC) bi - inlet enthalpy to cv. he: outlet enthalpy to mi = Rate of mass flowin into CV - O mes Ral of mens eriting control Volume condition: Also, due to adiabatic Qczo' ☺ so en 23 46 in O will give: deer co-(mcu) he +o- Wew idecu i mer he - wier] E2-E,= (ma-m) he -W 1-4 09: By integration wherer Final mass in cv. mg, m.= Initial & Eng Ep = final f initial inner energy We work produced by control volume Nale: he is constant since erit temperature is not changing ie. Te : 30 Constanta

Now: E=mcvT so, ea" (a1 becomes: (m2cv Iz- mi cvT) = (ma-m, The- w . To find mifma l mi: Initial meas of air in cui Pille. - m. - 500 x 1000 PV RJ, - 0.287 x 400 =43554 kg. Me: Final mass of air in cui

- P2 V2 V2= 0,= 10,000 m3 RTZ To find T2: For reversible adiabatic process for arv: 12. Y-119 fr=14 for cir? = (3.000.4114 50 IT2=345.68 K | : . mss. 300 x 10000 0.287 X 345.68 | Mz= 30238.81 kg | Also put Cp - 1.005 kJ 1ks 1, Cu: 0.718 kJ/ky 4 he: cpte, my, mz & he in egn © 32238.81 X 0.78 x 345.68 - 43554 X0.718 x 400 302 38.8)- 43554) X1-00 SX 300 - W Lw=-9 88 959.6 kJ Tw= 988.96MI)