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one mole of an ideal monatomic gas is caused to go through the cycle shown in Fig. 24-22. (a) How much work is done on the gas in expanding the gas from a to c along path abc? (b) What is the change in internal energy and entropy in going from b to c? What is the change in internal energy and entropy in going through one complete cycle? Express all answer in terms of the pressure p 0 and volume V 0 at point a in the diagram.
Dear student,Please find the solution to your problem. (a) W = – PΔV= – po(4Vo – Vo) = – 3poVoSo, Wabc = Wab = – 3poVoHence, work done on the gas in the path abc will be – 3poVo (b) The change in internal energy ΔEbc along the path b to c would be,ΔEbc = 3/2nRΔTbc= 3/2(nRTc – nRTb)= 3/2(PcVc – PbVb) [PV = nRT]= 3/2[(2po)(4Vo) – (po)(4Vo)]= 3/2 x 4poVo= 6poVoThe change in entropy ΔSbc along the path b to c would be ΔSbc = 3/2 nR ln(Tc/Tb)= 3/2 nR ln(Pc/Pb) [since, V remains constant from b to c hence, Tc/Tb = Pc/Pb]= 3/2 nR ln(2po/po)= 3/2 nR ln2 (c) The change in both internal energy and entropy would both be zero in a cyclic process. Thanks and regards,Kushagra
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