Question

[20 marks) 3 a) is the exergy of a system different in different environments? (2 marks) b) What is the second law efficiency? (2 marks) c) Consider a process during which no entropy is generated. Does the exergy destruction for this process have to be zero? (1 mark) d) A piston cylinder device initially contains 2 L of air at 100 kPa and 25 °C. Air is now compressed to a final state of 600 kPa and 150 °C. The useful work input is 12 kl. Assuming the surroundings are at 100 kPa and 25. determine The exerty of the air at the initial and final states The minimum work that must be supplied to accomplish this compression process, and The second law efficiency of this process

Answer 1

Date: Paga no: 3. Griven data:- soln Initial Pulsure and temperature, Pe = 100kPa f1=25€ (d) Final Pressure and temperature, P = 600k PO , TIE 150°C Volume of aix, V=2L = 0.002 m3 work input, Wein = 1.2 kJ Assumptions :- () Ait is an ideal gas with constant specific heats (2) The kinetic and potential eneegies are negligible Properties : From table A-L, The Geas constant of air is, R = 0.287 kPa - m²/kg.k The specific heats of ait at the average tembezature of (298+423) = 360 k are, (from table A-2) 2 Cp = 1-oog KJ/kg .k and Cr=0.722 kJ/kgk Analysis :-(i). we sealize that Xi = $1 = 0 Since air is at the dead state The mass of the ait is, m - PLVL (100 kPa) (0.002 m) RTI Co-287 kPami/kg.k) (298k) m = 0.00 234 kg AIR V=2L R=Lookpat T = 25°C

Date: Paga no:2 Also, P2 V2 PLVA T2 T 2 - Ps Tz Vt - P2 Te CLOok Pa)(423 k) (26) (600 kPa) (298) V2 - 0.473 L and S₂ - So = Cp,aug en Tz - R ln P2 To Po S2-So- (1009 kJ/k9K) en 423k -(0.287 kJ/kg k) en 6oo 298k 100 Sa-So - -0.1608 kJ/kgok Thus, the energy of air at the final state is, X2 = 02 = m [Crause (Tz-To) - To (52-5.)] + Pol V2-VO) = (0-00234 kg) [60.722 KJ/KG•K)(423-298) K - 298 K601660s hite) +(100 kPa) (О.0004 73 -0.002) m? [k5fm?kPa] -O.171 kJ Thus the exergy of the air at initial and final state is, os = 0 and 02 = 0.171 kJ

Date: Page no: 13 (11) The minimum work input is the reversible work input, which can be determined from the energy Balance by setting the excixgy destruction equal leto Zero, Net exergy transfer Exergy by heat , work, and mass destruction >(tweible) Xin - Xout X distroyed = AX system Change in exergy Wrew, in =X2-X. -0.171-0 Wrev, in = 0·171 kJ (in the second - love efficiency of this process is, no - Wrew in Wu, in 0.17L KJ 1-2 KJ no 14.3% (a) yes, exergy is a function of the state of the Ans Suttoundings as well as the state of the system. (b) The secand-lawe efficiency is a meassure of the Ans. Perfomance of a device relative to its Perfomance under reversible conditions. ins Yes, the excergy destruction for this process is Zeto,