nhiệt động học, nguyên lý ETROPY, định lý 2 NDHs

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ENTROPY – LAW OF THERMODYNAMICS ND OUTLINE • Reversible Process vs Irreversible Process • Quasi-Static vs Quick Process • Carnot’s theorem • Clausius’s Integration • Entropy • The Principle of Increase of Entropy • The Change in Entropy of an Ideal Gas REVERSIBLE – IRREVERSIBLE PROCESS In a reversible process, the system can be returned to its initial conditions along the same path on a PV diagram, and every point along this path is an equilibrium state A process that does not satisfy these requirements is irreversible P P 1 Quasi–static process irreversible Quick (sudden) process 2 irreversible reversible V V QUASI-STATIC vs QUICK PROCES P P Quasi–static process Quick (sudden) process 2 irreversible reversible V V Carnot's theorem Carnot's theorem, developed in 1824 by Nicolas Léonard Sadi Carnot, also called Carnot's rule, is a principle that specifies limits on the maximum efficiency any heat engine can obtain Carnot's theorem states: • All heat engines between two heat reservoirs are less efficient than a Carnot heat engine operating between the same reservoirs • Every Carnot heat engine between a pair of heat reservoirs is equally efficient, regardless of the working substance employed or the operation details Tc emax  eCarnot   Th CARNOT ENGINE Two reservoirs, temperature Th, Tc e  ecarnot Q' T 1 c  1 c Qh Th Q' T  c  c Qh Th Qc Q  h Tc Th Qh Qc  0 Th Tc CLAUSIUS’S INEGALITY Qj, Tj P Divide any reversible cycle into a series of thin Carnot cycles, where the isothermal processes are infinitesimally short: Qi, Ti V   reversiblecycle Qi   T   irriversiblecycle i i     reversiblecycle  0 T   irriversible cycle Q  ENTROPY   reversiblecycle  0 T   irriversible cycle Q Consider a reversible cycle 1a2b1 The Clausius integration has sign “=“ P Q  a b 1a 2b1  1a V Definition: We define a state variable S that the change in the entropy dS is equal to the heat received in a reversible process divided by the absolute temperature of the system  1a T Q T Q T  0   Q T 2b1   Q 2b1 Q 1a _ rever T  S  0 T   1b _ rever Q 12 _ reversible dS  Qrev T T Q T ENTROPY (Cont.) Consider an irreversible cycle 1a2: irreversible 2b1: reversible The Clausius integration has sign “ the change in entropy during a process depends only on the endpoints => the change in entropy is independent of the actual path followed Consequently, the entropy change for an irreversible process can be determined by calculating the entropy change for a reversible process that connects the same initial and final states The principle of Increase of Entropy Qrev S12   T 12 S may be >0; S12  0  reversible_ process S > 0, for irreversible processes S = 0, for reversible processes S < 0, the process is impossible The entropy of the Universe increases in all real processes The Change in Entropy of an Ideal Gas dS  Qrev T dU  Q  PdV Q  dU  PdV dU  PdV i nRdT nR dS    dV T T V T2 V i nRdT nR S    dV T1 T V1 V T2 V  nR ln T1 V1 PV V  nCv ln 2  nR ln P1V1 V1 P V V  nCv ln  nCv ln  nR ln P1 V1 V1  nCv ln P2 V2 S  nCv ln  nCp ln P1 V1 i U  nRT; PV  nRT i Cv  R i2 Cp  R  Cv  R The Change in Entropy of an Ideal Gas Isothermal Process dQ Q12   T T S   V2 V1 T  nR ln V2 V1 nCvdT T2 S    nCv ln T T1 Isovolumetric Process nC dT p S   Isobaric Process Adiabatic Process nRTln S  T  nCp ln S  const T2 T1 Iso_entropy Process Example 22.6 Change in Entropy: Melting A solid that has a latent heat of fusion Lf melts at a temperature Tm Calculate the change in entropy of this substance when a mass m of the substance melts dQ S   T T  Tmelt  Const Q mLf S   T Tmel Entropy trao đổi, entropy tạo Độ biến thiên entropy hệ Entropy trao đổi Q: nhiệt mà hệ nhận Tnguon nhiet: Nhiệt độ nguồn nhiệt Entropy tạo S  Straodoi  Stao _ Q S   T Q Straodoi  Tnguon _ nhiet Stao _  S  Straodoi Stạo =0: q trình Thuận nghịch Stạo >0: q trình Khơng Thuận nghịch ... 1a 2irr 2b1rev Q Q  T  T 1a _ irr 1b2 _ rev Q  T  S 1 2rev Q S   T 1a _ irr ENTROPY S • Entropy S is a state variable S  S2  S1  State_  State_1 P a b V S1a 2irrev  S1b2rev...  0   Q T 2b1   Q 2b1 Q 1a _ rever T  S  0 T   1b _ rever Q 1 2 _ reversible dS  Qrev T T Q T ENTROPY (Cont.) Consider an irreversible cycle 1a2: irreversible 2b1: reversible... nRdT nR dS    dV T T V T2 V i nRdT nR S    dV T1 T V1 V T2 V  nR ln T1 V1 PV V  nCv ln 2  nR ln P1V1 V1 P V V  nCv ln  nCv ln  nR ln P1 V1 V1  nCv ln P2 V2 S  nCv ln  nCp ln P1