Question

11. Three moles of an ideal gas are initially confined to 3.45x10- mat 1.06x106 Pa. A. Calculate the total work involved in a four-step isothermal and irreversible expansion, where Step 1: Pext = 7.35x10 Pa Step II: Pext = 5.12x105 Pa Step III: Pext = 3.56x10 Pa Step IV: Pext = 1.78x109 Pa B. Calculate the total work (starting from the same initial state) for an isothermal and reversible expansion to 1.78x10 Pa. C. Construct a computer-generated PV plot for the expansions in Part A and Part B. Indicate on the plot the difference in area between Part A and Part B.

Answer 1

242 na 3 mole = 3.45 x 103 m3 Pin= 1.06100pa Pin= Pinitial OT A Step I Pext = 7.35 10 Spa For isothermal and ineversible exponeron Wim -Pext ( Vf - vi) = -lent --PF CHAT - NAT) Perts pf Win -ORT (1-P fetons fan final Wisor (Steri) - 3*8.314 XT(I 7-354105 ) = -7.6477 Joule 06106 Win (Steps ) - 38714T/1 = 542 1057 104105 ) = -12.9941 Joule 8 8314 AT (I- 3.560 105 1060 106) =-16.565 T Joule win (step ats) = -308.8314 AT (1-3 With (Stepstva - 318 314 I 1-78x105 ja -20.754 OT Jouk TOG 101 2 05OT Jout Total worked involved = (-7.647 - 12.894. - 16.565- 20.754)T Jone With - 57.68 T Joule (Tin Kelvin) B for isothermal revereible expansion Wrew = nRT ln (2) = -3 mol x 8.314 Jky moly tk ln (Pi) 59-24.942 In 1-06790 6 pa C 1.78 xins & T Joule = -44.50T Joule For isothermal reversikt expansion W=-S rex du Wre – JPau (Tinkelvin) For othermal bone vereihe expansion 1 ,0 Pressure P2 - Irreverable work done anca Renwork area But here 4 eteps are involved its PIVIT) II (P21V2,T) 355, V3,) Volume 2 VA (P <p> VET) Arrea (A) (pant) 4 H PA Single step process revwork done area>ion ! But here in part (B) 4 steps are involved so herea part (B) are a Chould be greater than park A. were revwork done area ion work done area Area ( Part B2