1. C Applications of the Second Law N-Chapter6;VWB&S-8.1,8.2,8.5,8.6,8.7,8.8,9.6] 1. CI Limitations on the work that Can be supplied by a heat engine The second law enables us to make powerful and general statements concerning the maximum work that can be Q1 derived from any heat engine which operates in a cycle. To illustrate these ideas, we use a Carnot cycle which is shown schematically at e right. The engine operates between two heat Carnot cycle r reservoirs, exchanging heat QH with the high temperature reservoir at Ti and e, with the reservoir at TL. The entropy changes of the two reservoirs are AS,= Q Q The same heat exchanges apply to the system, but with opposite signs; the heat received from the high temperature source is positive, and conversely. Denoting the heat transferred to the engines by subscript“e”, The total entropy change during any operation of the engine is, ASL+△S Re servo at TH For a cyclic process, the third of these(As ) is zero, and thus(remembering that QH <0), atotal=As, AS,= QH 2r (C.1.1) For the engine we can write the first law as AUe=0(cyclic process)=QHe +OLe -We W Q1 Hence, using(C1.1) We=-QH-7i4Slotal eH\TH IC-11C-1 TH QH We QL TL Carnot cycle 1.C Applications of the Second Law [VN-Chapter 6; VWB&S-8.1, 8.2, 8.5, 8.6, 8.7, 8.8, 9.6] 1.C.1 Limitations on the Work that Can be Supplied by a Heat Engine The second law enables us to make powerful and general statements concerning the maximum work that can be derived from any heat engine which operates in a cycle. To illustrate these ideas, we use a Carnot cycle which is shown schematically at the right. The engine operates between two heat reservoirs, exchanging heat QH with the high temperature reservoir at TH and QLwith the reservoir at TL.. The entropy changes of the two reservoirs are: ∆S Q T H Q H H = < H ; 0 ∆S Q T L Q L L = > L ; 0 The same heat exchanges apply to the system, but with opposite signs; the heat received from the high temperature source is positive, and conversely. Denoting the heat transferred to the engines by subscript “e”, Q QQ Q He =− =− H Le L ; . The total entropy change during any operation of the engine is, ∆ ∆ ∆∆ S S SS total H servoir at TH L servoir at TL e Engine =++ Re Re { { { For a cyclic process, the third of these ( ) ∆Se is zero, and thus (remembering that QH < 0), ∆ ∆∆ S SS Q T Q T total H L H H L L = + =+ (C.1.1) For the engine we can write the first law as ∆U Q QW e He Le = = +− e 0 (cyclic process) . Or, WQ Q e He Le = + = − − Q Q H L . Hence, using (C.1.1) W Q TS Q T T e HL total H L H =− − +      ∆ 