Contents of Today S.J.T.0. Phase Transformation and Applications Review previous Second law Functions F and G Property relation Property relation derived from U,H,F,and G etc. SJTU Thermodynamics of Materials Fall 2012 X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation Contents of Today Review previous Second law Functions F and G Property relation Property relation derived from U, H, F, and G etc
熵增原理 S.J.T.0. Phase Transformation and Applications 卡诺定理/可用热力学第二定律证明 +s1- 式中Q2为从高温热源吸热 92 T2 Q1为向低温热源放热 1+2≤0 克劳修斯等式（可逆）和不等式( T T2 不可逆过程) 更普遍的循环过程 ≤0 δQ为为系统从温度为T的热源吸取的热量 可逆过程的热温商为零，所定义的熵为状态函数 SJTU Thermodynamics of Materials Fall 2012 X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation 熵增原理 卡诺定理 / 可用热力学第二定律证明 21 1 2 2 QQ T 1 Q T η + = ≤− 式中Q2为从高温热源吸热 Q1为向低温热源放热 1 2 1 2 Q Q 0 T T + ≤ 克劳修斯等式（可逆）和不等式（ 不可逆过程） Q 0 T δ ∫ ≤ 更普遍的循环过程 δQ为为系统从温度为T的热源吸取的热量 可逆过程的热温商为零，所定义的熵为状态函数
熵增原理一热力学第二定律的普遍描述 S.J.T.0. Phase Transformation and Applications δQ为为系统从温度为T的热源吸取的热量 <0 可逆过程的热温商为零，所定义的熵为状态函数 设系统由初态A变为终态B,设系统经过一个 设想的可逆过程由状态B回到状态A 9+≤0 -5.-Sa sas≥归9 热力学第二定律对过程的限制，违反上述不等式的过程是不可能发生的！ SB-SA≥0 绝热条件下 SJTU Thermodynamics of Materials Fall 2012 X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation 熵增原理－热力学第二定律的普遍描述 Q 0 T δ ∫ ≤ δQ为为系统从温度为T的热源吸取的热量 可逆过程的热温商为零，所定义的熵为状态函数 A B 设系统由初态A变为终态B，设系统经过一个 设想的可逆过程由状态B回到状态A B A rev A B Q Q 0 T T δ δ ∫ ∫ + ≤ A rev A B B Q S S T δ ∫ = − B B A A Q S S T δ − ≥ ∫ 热力学第二定律对过程的限制，违反上述不等式的过程是不可能发生的！ SS0 B A − ≥ 绝热条件下
Summary S.J.T.0. Phase Transformation and Applications Some heat must be discarded into a cold sink in order for Hot Source us to generate enough Entropy falls entropy to overcome the Heat withdrawn decline taking place in the hot reservoir Surroundings Energy stored at a high Work temperature has a better Heat dumped quality:high-quality energy Cold sink Entropy is available for doing work; increases low-quality energy,corrupted energy,is less available for doing work冬季取暖/进化 SJTU Thermodynamics of Materials Fall 2012 ©X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation Some heat must be discarded into a cold sink in order for us to generate enough entropy to overcome the decline taking place in the hot reservoir Energy stored at a high temperature has a better “quality”: high-quality energy is available for doing work; low-quality energy, corrupted energy, is less available for doing work冬季取暖/进化 Summary
热力学第二定律几点说明！ S.J.T.0. Phase Transformation and Applications 过程 研究过程方向问题（任务）《 一不可能的过程 一体系十环境（孤立体系熵增 一可能的过程 原理)《一热力学第二定律( 基础但不好用) ·可逆 ·不可逆（自发）过程 熵为体系的状态函数/平衡状态 B SJTU Thermodynamics of Materials Fall 2012 X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation 热力学第二定律几点说明！ 过程 – 不可能的过程 – 可能的过程 • 可逆 • 不可逆（自发）过程 熵为体系的状态函数/ 平衡状态 研究过程方向问题（任务）《 －体系＋环境（孤立体系熵增 原理）《－热力学第二定律（ 基础但不好用） TI TII A B
2.9 Entropy Changes(2) S.J.T.0. Phase Transformation and Applications 变化过程的 熵很重要， 所以要计算 H=AH △H= C Temperature S= dT △S P(S) Temperature SJTU Thermodynamics of Materials Fall 2012 X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation 2.9 Entropy Changes (2) ∫ Δ = Tm T P S dT T C S 1 ( ) ∫ Δ = Tm T P l dT T C S 1 ( ) m m m T H S Δ Δ = Temperature Entropy ∫ Δ = Tm T H CP S dT 1 ( ) ∫ Δ = Tm T H CP l dT 1 ( ) ΔH = ΔH m Temperature Enthalpy 变化过程的 熵很重要， 所以要计算
2.10 Entropy change in chemical reactions and the third law(1) S.J.T.0. Phase Transformation and Applications The calculation of entropy changes for a chemical reaction is similar to the calculation in the case of enthalpy changes. One very important difference: Nernst 1906 The entropy change in any chemical reaction involving only pure,crystalline substances: ZERO at the ABSOLUTE Zero of temperature. Pure:pure elements and stoichiometrically balanced compounds that are perfectly crystalline Planck The entropy of a pure,perfectly crystalline substances ZERO at the ABSOLUTE Zero of temperature. Superscript zero:standard state,1 atm △D =0 Subscript zero:temperature ZERO SJTU Thermodynamics of Materials Fall 2012 X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation 2.10 Entropy change in chemical reactions and the third law (1) The calculation of entropy changes for a chemical reaction is similar to the calculation in the case of enthalpy changes. One very important difference: Nernst 1906 The entropy change in any chemical reaction involving only pure, crystalline substances: ZERO at the ABSOLUTE Zero of temperature. Pure: pure elements and stoichiometrically balanced compounds that are perfectly crystalline. Planck The entropy of a pure, perfectly crystalline substances: ZERO at the ABSOLUTE Zero of temperature. 0 0 ΔS0 = Superscript zero: standard state, 1 atm Subscript zero: temperature ZERO
2.10 Entropy change in chemical reactions and the third law(2) S.J.T.0. Phase Transformation and Applications The third law provides a great simplification in the calculation of entropies of reaction Ag-A心+f9an-f9n The entropy changes near room temperature are often needed in thermodynamic calculations, the integral in above equation has been evaluated for many substance at 298 K. 298 S98= △H+了 -dT 0 T SJTU Thermodynamics of Materials Fall 2012 X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation 2.10 Entropy change in chemical reactions and the third law (2) The third law provides a great simplification in the calculation of entropies of reaction. ∫ ∫ Δ = Δ + = T P T P T dT TC dT TC S S 0 0 00 0 The entropy changes near room temperature are often needed in thermodynamic calculations, the integral in above equation has been evaluated for many substance at 298 K. ∫ ∫ ∫ + Δ + + Δ = + 298 0 0 298 b b m m T P T T b P b m m T P dT T C T H dT T C T H dT T C S
Index of nomenclature S.J.T.0. Phase Transformation and Applications Helmholtz free energy(F):亥姆赫茨自有能 Gibbs free energy(G):吉布斯自有能 Chemical potential:化学位 SJTU Thermodynamics of Materials Fall 2012 ©X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation Index of nomenclature Helmholtz free energy (F): 亥姆赫茨自有能 Gibbs free energy (G): 吉布斯自有能 Chemical potential：化学位 Index of nomenclature
Chap 3 Property Relations S.J.T.0. Phase Transformation and Applications The First Objective:to explore the variation of the energy functions(U and H) with temperature and pressure. The heat capacities(Cp and Cv)give the change of U and H with temperature, at constant volume and constant pressure,respectively. The Second Objective:to examine the dependence of properties,such as the internal energy,enthalpy,entropy,and other thermodynamic functions,on temperature,pressure,specific volume,and other intensive variables. P SJTU Thermodynamics of Materials Fall 2012 ©X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation Chap 3 Property Relations The First Objective: to explore the variation of the energy functions (U and H) with temperature and pressure. The heat capacities (Cp and Cv) give the change of U and H with temperature, at constant volume and constant pressure, respectively. The Second Objective: to examine the dependence of properties, such as the internal energy, enthalpy, entropy, and other thermodynamic functions, on temperature, pressure, specific volume, and other intensive variables. 2 1 B A V T T V U ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ T V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ 2 1 B A P T P T H ⎟⎠⎞ ⎜⎝⎛ ∂∂ T P H ⎟⎠⎞ ⎜⎝⎛ ∂∂