Chapter 4 thermodynamic functions and fundamental equations

34 303 0
Chapter 4   thermodynamic functions and fundamental equations

Đang tải... (xem toàn văn)

Tài liệu hạn chế xem trước, để xem đầy đủ mời bạn chọn Tải xuống

Thông tin tài liệu

Internal energy U: minimum at a given S, V. Entropy S: maximum at a given U, V. Gibbs function G: minimum at a given T, P. Helmholtz function F: minimum at a given T, V. Enthalpy H: minimum at a given S, P.

PHYSICAL CHEMISTRY ChapterThermodynamic functions and Fundamental equations Ngo Thanh An Part – Thermodynamic functions Thermodynamic functions Thermodynamic function Symbol Definition unit Gibbs free energy (isothermal, isobaric thermodynamic potential) G G = H –TS Cal or J Helmholtz free energy (isothermal, isochoric thermodynamic potential) F F = U – TS Cal or J Entropy S dS=Qrev/T cal.K–1 J.K–1 Internal energy U Enthalpy H Cal or J H = U + PV Cal or J Thermodynamic functions � U� � T � � ��S � V U� �� H  U  PV  U  V � � V� �� S � U� � P  � � ��V � S U � �� U� �� G  H  TS  U  V � � S� � V� S� �� �� S V ��2U � � U� � CV  � � � � F  U  TS  U  S� � ��S � V ��S � ��S � V V ��U � Characteristics of thermodynamic functions • • • • • Internal energy U: minimum at a given S, V Entropy S: maximum at a given U, V Gibbs function G: minimum at a given T, P Helmholtz function F: minimum at a given T, V Enthalpy H: minimum at a given S, P Characteristics of thermodynamic functions Characteristics of thermodynamic functions Chứng minh Theo nguyên lý tăng entropy, entropy đạt cực đại thì: Ta đặt giá trị A bằng: Vậy A bằng: Ta lại có: Áp dụng cơng thức: Characteristics of thermodynamic functions Chứng minh Vậy giá trị A 0, tức U đạt cực trị theo V giá trị entropy Ta xem A hàm số A = A(V, U(V)) Tính chất đạo hàm hàm hợp cho ta công thức: Như vậy, ta có: Với điều kiện A = 0, cho ta: Characteristics of thermodynamic functions Chứng minh Như vậy, hàm U đạt cực tiểu Relations of thermodynamic functions Legendre transform If we have a function F = F(x,y) We need to transform function F(x,y) into:  Function G(x,w) where w is a conjugate variable of variable y  Function H(u,y) where u is a conjugate variable of variable x  Function L(u,w) where u, w are conjugate variables of x, y respectively Prove: where: (1) (2) Equation (1) – equation (2), having : Where Relations of thermodynamic functions Maxwell relations c Gibbs • Trongtrườnghợpápdụngphươngtrình   chohàm F: • Ta sẽcó: d Trongtrườnghợpápdụngphươngtrình Gibbs chohàm G: • Ta sẽcó: Effect of thermodynamic properties Summary Effect of thermodynamic properties Internal Energy Changes 22 Effect of thermodynamic properties 23 Effect of thermodynamic properties Enthalpy Changes 24 25 Effect of thermodynamic properties Entropy Changes 26 Joule – Thomson coefficient The temperature behavior of a fluid during a throttling (h = constant) process is described by the Joule-Thomson coefficient The Joule-Thomson coefficient represents the slope of h = constant lines on a T-P diagram The temperature of a fluid may increase, decrease, or remain constant during a throttling process The development of an h = constant line on a P-T diagram Joule – Thomson coefficient Constant-enthalpy lines of a substance on a T-P diagram A throttling process proceeds along a constant-enthalpy line in the direction of decreasing pressure, that is, from right to left Therefore, the temperature of a fluid increases during a throttling process that takes place on the right-hand side of the inversion line However, the fluid temperature decreases during a throttling process that takes place on the left-hand side of the inversion line It is clear from this diagram that a cooling effect cannot be achieved by throttling unless the fluid is below its maximum inversion temperature This presents a problem for substances whose maximum inversion temperature is well below room temperature Part – Fundamental equations Fundamental equations The equation is obtained by combining the first and second law of thermodynamics a) First law of thermodynamics: dU = Q - A Second law of thermodynamics Q dS � T dU  T.dS - A 30 Fundamental equations but: A = P.dV +  A’ P.dV : mechanic work A’ : other works (useful works)  dU  T.dS – P.dV – A’ If process is reversible: dU = TdS – PdV –  A’max 31 Fundamental equations b) H = U + PV  dH = dU + PdV + VdP  dH  T.dS – P.dV - A’ + PdV + VdP  dH  TdS + VdP – A’ If process is reversible: dH = TdS + VdP –  A’max c) G = H – TS = U + PV – TS  dG = dH – TdS - SdT  dG  – SdT + VdP – A’ If process is reversible: dG = – SdT + VdP –  A’max Fundamental equations d) F = U – TS  dF = dU – TdS - SdT  dF  – SdT – PdV – A’ If process is reversible: dF = – SdT – PdV –  A’max “

Ngày đăng: 26/02/2018, 22:14

Từ khóa liên quan

Mục lục

  • Slide 1

  • Slide 2

  • Slide 3

  • Slide 4

  • Slide 5

  • Slide 6

  • Slide 7

  • Slide 8

  • Slide 9

  • Slide 10

  • Slide 11

  • Slide 12

  • Slide 13

  • Slide 14

  • Slide 15

  • Slide 16

  • Slide 17

  • Slide 18

  • Slide 19

  • Slide 20

  • Slide 21

  • Slide 22

  • Slide 23

  • Slide 24

  • Slide 25

  • Slide 26

  • Slide 27

  • Slide 28

  • Slide 29

  • Slide 30

  • Slide 31

  • Slide 32

  • Slide 33

  • Slide 34

Tài liệu cùng người dùng

  • Đang cập nhật ...

Tài liệu liên quan