Chapter 2 The First Law 2.1 The basic concepts Thermodynamics field of physics that describes and correlates the physical properties of macroscopic systems of matter and energy System and surrounding  System the parts of the world in which we have a special interest.  Surroundings where we make our measurement.

system water Open system system water+ vapor Closed system systemwater+gas Isolated system adiabatic

2.1.2 Thermodynamic properties Pressure p, volume temperature V, temperature T, internal energy U, enthalpy H, entropy S …… extensive property = intensive property e.g. e.g mass, volume  Extensive property a property that depends on the amount of substance in the sample. e.g. Temperature ， pressure ， density  Intensive property a property that is independent of the amount of substance in the sample.

2.1.3 Definition of phase  Phase a homogeneous part of a system. Homogeneous system one phase Heterogeneous system two or more phase, interface The equilibrium state Thermal equilibrium T 1 = T 2 = T 3 =… = T ex Mechanical equilibrium p 1 = p 2 = p 3 =… = p ex Phase equilibrium   =   =   =… Chemical equilibrium  A =  B =  Y =  Z … Thermodynamic state—— equilibrium state ：

2.1.5 State and state function The value of a state function depends only on the present state of the system and not on its past history. The state of a macroscopic system in equilibrium can be described in terms of such measurable properties as T, p, and V, which are known as thermodynamic variables( or state functions). State description Classical mechanics: Thermodynamics: p,V,T…

2.1.6 Process and path  Process When a macroscopic system moves from one state of equilibrium to another, a thermodynamic process is said to take place.  Path (b)Isobaric process p 1 = p 2 ＝ p ex (a)Isothermal process T 1 = T 2 ＝ T ex (c)Isochoric process V 1 = V 2 (d)Adiabatic process Q=0 (e)Cyclic process 1. p, V, T process

(f)expansion against constant pressure p ex =constant (g) free expansion pressure p ex =0

2. Phase transition process

aA + bB = yY + zZ 0 = Σ B B n B,0 is the number of mole of substance B present at the start of the reaction. 3. Chemical reaction process B —stoichiometric number of B  n B = n B,0  n B = B  ， d n B = B d  A = － a ， B = － b ， Y = y, Z = z extent of reaction — , units is mol 。

2.1.7 Work and heat W>0 W is done on the system by the surroundings W <0 system does work on its surrounding  Work The energy transfer between system and surroundings due to a macroscopic force acting through a distance  Heat The energy transfer between system and surroundings due to a temperature difference Q>0 when heat flows into the system from the surroundings Q<0 when heat flows into the surroundings from system

2.1.8 Internal energy U Type of work dWdWdWdW Expansion Surface expansion Electrical -p ex dV  dA  dA  dq (2) U is an extensive property; (1) U is state function ; (3) the absolute value of U is unknown. The total energy of system

2.2 The first law  U =U 2 － U 1 = Q + W closed system dU＝δQ＋δWdU＝δQ＋δW U＝Q＋WU＝Q＋W Isolated system Cyclic process Adiabatic process Q=0, W=0,  U=0  U=0, Q=  W Q =0,  U = W  Conservation of energy  It is impossible to built a first kind of perpetual motion machine.  Work and heat dU =  Q +  W

2.2.1 Expansion work 1.Free expansion p ex =0, W=0

2.Expansion against constant pressure

3. Reversible expansion  Different expansion Different expansion  Reversible expansion  W= - p ex dV = - pdV  Quasi-static process

 Isothermal reversible expansion Consider the isothermal, reversible expansion of a perfect gas:

 Reversible process One where the system is always infinitesimally close to equilibrium and an infinitesimal change in conditions can reverse the process to restore both system and surroundings to their initial state. Characteristic (a) Infinitesimally close to equilibrium. (b) T ex ＝ T ； p ex ＝ p. (c) Both system and surroundings can be restore to their initial state through reverse process.

2.2.2 Heat transaction Consider closed system dU =  Q +  W =  Q +  W exp +  W’ dV=0,  W’=0, dU =  Q V,  U = Q V (a) Calorimetry A constant-volume bomb calorimeter. The `bomb' is the central vessel, which is massive enough to withstand high pressures. The calorimeter is the entire assembly shown here. To ensure adiabaticity, the calorimeter is immersed in a water bath with a temperature continuously readjusted to that of the calorimeter at each stage of the combustion.

Definition of molar heat capacity (b) Heat capacity Molar heat capacity at constant volume

(c) Enthalpy W ＝－ p ex  V W ＝－ p ex  V, W′ ＝ 0 ，  U = Q p － p ex  V U 2 － U 1 = Q p － p ex (V 2 － V 1 ) p 1 = p 2 = p ex U 2 － U 1 = Q p － (p 2 V 2 － p 1 V 1 ) Q p = (U 2 ＋ p 2 V 2 ) － (U 1 ＋ p 1 V 1 ) =  (U ＋ pV) Isobaric process

(1) H is state function ; (2) H is an extensive property; (3) the absolute value of U is unknown.  Enthalpy For a closed system, p=const. W ’ =0 Q p =  H δQ p = dH

C p ， m ＝ a ＋ bT ＋ cT 2 ＋ dT 3 or C p ， m ＝ a ＋ bT ＋ c′T － 2 approximate empirical expression Molar heat capacity at constant pressure Perfect gas C p,m -C V,m =R

Adiabatic changes dU ＝ C V dT, dU ＝  W if C V,m =const. W ＝  U = n C V,m (T 2 － T 1 ) (a) The work of adiabatic change dU ＝ δW, if δW′ ＝ 0 then C V dT ＝－ p ex dV Reversible process, p ex ＝ p, perfect gas

perfect gas C p － C V ＝ nR perfect gas γ=constant (b) heat capacity ratioγ and adiabats ln{ T } ＋ (γ  1) ln{ V } = constant TV γ-1 = constant ( perfect gas, reversible process, closed system, W ′ ＝ 0.) Equations of adiabatic reversible process

pV  =constant (c) Work of adiabatic reversible process of perfect gas

2.2.4 Phase transition 1. Enthalpies of phase transition T=const., p =const.,W'=0 vaporization :  vap H m, fusion :  fus H m, sublimation :  sub H m, transition:  trs H m Enthalpy of

2. Expansion work of phase transition at constant T and p W ＝－ p(V  － V  ) β-gas phase,α-liquid phase (or solid phase) V  >>V , W  － pV β β perfect gas W ＝－ pV β ＝－ nRT

3.  U of phase transition U ＝ H －p(Vβ－Vα)U ＝ H －p(Vβ－Vα) V β >>V α,  U ＝  H － pV β perfect gas  U ＝  H － nRT U ＝Qp＋WU ＝Qp＋W

2.3.1 Molar enthalpies and internal energies of chemical change aA + bB = yY + zZ 2.3 Thermochemistry Standard enthalpy changes Standard molar enthalpies of the substance B at temperature T and pressure p 。 (B=A, B, Y, Z;  =phase state)

2.3.3 Standard states of substances Standard pressure p  ＝ 100kPa gas:p = p , T, perfect gas solid or liquid : p ex = p , T  r H m  (T) = yH m  (Y, , T ) ＋ z H m  (Z, , T ) － a H m  (A, , T ) － b H m  (B, , T ) For reaction aA ＋ b B →yY ＋ zZ Pure, unmixed reactant in their standard states  Pure, separated products in their standard states

2.3.4 Relation between  r H m and  r U m For a reaction  r H m (T, liquid or solid) ≈  r U m (T, l or s)  r H m ( T) ＝  r U m (T) ＋ RT  B (g)  r H m (T) ＝  B H m (B, , T ) ＝  B U m (B, ,T ) ＋  B [p V m (B,T)] T= Constant V=constant W′ ＝ 0 Q V ＝  r U T= Constant p=constant W′ ＝ 0 Q p ＝  r H

2.3.5 Hess’s law AC B  r H m (T ) =  r H m,1 (T ) ＋  r H m,2 (T ) The standard enthalpy of overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided.

 r H m (T) in term of  f H m (B, ,T )  r H m (T) =  B  f H m (B, ,T ) reactan ts elements products  r H m Enthalpy, H Standard enthalpies of formation  f H m (B, ,T )

 r H m (T)in term of  c H m (B, ,T )  r H m (T) = –  B  c H m (B, ,T ) * reactant s CO 2 (g), H 2 O(l) products  r H m Enthalpy, H Standard molar enthalpies of combustion  c H m (B,phase state,T )

2.3.8 The temperature dependence of reaction enthalpies aAaA + bBbB yYyY + zZzZ aAaA + bBbB yYyY + zZzZ  r H m (T 1 ) =  H 1 ＋  H 2 ＋  r H m (T 2 ) ＋  H 3 ＋  H 4

 B C p,m (B)=yC p,m (Y) ＋ zC p,m (Z) - aC p,m (A)- bC p,m (B) If T 2 ＝ T,T 1 ＝ K, Kirchhoff’s law

2.4 State function and exact differentials Exact differentials Z = f (x, y ), Internal energy U = f (T, V ), The Joule experiment

Perfect gas dU=C V dT, or U=f(T) Enthalpy H = f (T, p ), dH=C p dT, or H=f(T)Perfect gas

2.4.4 The Joule-Thomson effect Q＝0Q＝0  U ＝ W or U 2 － U 1 ＝ p 1 V 1 － p 2 V 2 U 2 ＋ p 2 V 2 ＝ U 1 ＋ p 1 V 1 H 2 ＝ H 1 W＝p1V1－ p2V2W＝p1V1－ p2V2 Isenthalpic process U ＝ f(T)

Joule-Thomson coefficient  p ＜ 0,  J-T ＜ 0, heating ；  J-T ＞ 0, cooling ；  J-T ＝ 0, T unchanged