(The First Law of Thermodynamics)

1. 1st thermodynamics law & its application

U = Q -W

Content1.1          Introduction to thermodynamics

1.2          1st thermodynamics law

1.3          Quasi-static & reversible process

1.4          Enthalpy

1.5          Heat capacity

1.6          Application

1.7          Real gases

1.8         Thermal chemistry

1.9          Hess’s law

1.10        Several thermal effects

1.11        Kirchoff law

1.1 Introduction to thermodynamics• Research the interactive transformation among the heat,

work and other form energy.• Research the energy effect which takes place in the

different physical and chemical changes;• Research the direction and limitation of chemical

changes.• The mechanics, rate and microcosmic properties are

unknown, so we only think the possibility but the reality.

1.1.1 System and surroundingsSystem We call the fixed research object as

system, also substance system. System is separated from the other parts, the boundary can be visual or imaginable.

Surroundings The part which has reciprocity with

system, or correlate with the system closely.

1.1.1.1 Open system

Both matter and energy exchange take place between system and surroundings.

1.1.1.2 Closed system

It has no matter exchange, but energy exchange between system and surroundings.

1.1.1.3 Isolated system • Neither matter nor energy

exchange takes place between system and surroundings.

• Sometimes both the closed system and its surroundings are thought as an isolated system.

1.1.2 System properties The macrocosmic measurable properties are

used to describe thermodynamics state of the system, so all these properties are called thermodynamics variables.

1.1.2.1 Extensive properties (capacity properties)

Numerical value is directly ratio with system quantity, volume (V), entropy (S). These properties can be summed up.

1.1.2.2 Intensive properties• Its numerical value depends on its

own character of the system, it has nothing to do with the quantity of system. T, P.

• The capacity properties of every mole material quantity are designated as intensive properties, such as molar heat capacity.

1.1.3 Thermodynamic equilibrium

• Thermal equilibrium

• Mechanical equilibrium

• Phase equilibrium

• Chemical equilibrium

1.1.4 State function Some values of system

properties have nothing to do with the history of the system, they are decided by system state. The change values depend on the initial and the final state, and have nothing to do with the change ways. This kind of physical quantity is called state function.

1.1.4.2 State function characters

• Different ways come to the same final, the value change is the same ;– 异途同归，值变相等；

• Move one cycle, numerical value go back to the origin.– 周而复始，数值还原。

• In mathematics, State function has the character of full differential.

1.1.5 Heat and work

1.1.5.1 Heat The energy transfers from system to

surrounding because of the different temperature. Q stands for heat.

System absorbs heat, Q>0; System gives out heat, Q<0.

1.1.5.2 Work • Except for heat, any other energy transformation

forms from system to surrounding. • W stands for work.• System export work to surrounding, W>0;• Surrounding export work to system, W<0.• Both Q and W are not state function, their

numerical value is related with the change ways

fdldVpdVW Af

1.2 The first law of thermodynamics

1.2.1 Heat equivalent of work

• From 1840, Joule and Mayer had confirmed the relationship of heat and work by many different experiment: 1 cal=4.1840 J

• Energy conversation law: In the nature, every substance has energy, which has different change forms. It can change from one form to another, but during the change, the total energy is unchangeable.

1.2.2 Thermodynamics energy• Thermodynamic energy (internal energy):

the summation of system internal energy. It includes the translation energy of the molecule motion, and molecule internal energy.

• Thermodynamics energy is state function, U stands for it, its absolute value is unknown. We can only work out its change value.

1.2.3 The first law of thermodynamics U = Q -W dU =Q -W • Energy conservation and translation law have

special forms in the area of heat phenomena, it

shows that thermodynamic energy, heat and work

can change each other. • The 1st kind of the perpetual machine can not be

made-up. • ( It does not need environment to provide energy, but can

export work perpetually.)

1.3 quasi-static process & reversible process

Work and process

quasi-static process

Reversible process

1.3.1 Work and process The system volume expands from V1 to V2.

through 4 different ways. T = constant; outside pressure pe; work material: the fixed ideal gas.

1.3.1.1 Free expansion

0 dVpW e

)( 122, VVpW ee

1.3.1.2 The same temperature expansion

1.3.1.3 Expansion many times at the same pressure

1. The system volume expand from V1 to V’ by conquering the outside pressure P’ ;

2. The system volume expand from V’ to V” by conquering the outside pressure P” ;

3. The system volume expand from V” to V2

by conquering the outside pressure P2 .)()"()( "

22'"

1''

3, VVpVVpVVpWeee

1.3.1.3 Page 2• The work of the system

equals to the summation work of the three process.

• The more the times of expansion,The less difference between system and outside pressure, the more it works.

1.3.1.4 Outside press is infinite smaller than inside press

Work: dVpW ee 4, dVdppi )(

dVpV

V i 2

1

dVV

nRTV

V 2

1

2

1

lnV

nRTV

This process can approximately be regarded as a reversible process, the work is the most.

1.3.1.5 Compress process

Compress the volume from V1 to V2, It has three ways as following:

1.3.1.5.1 Compress at constant pressure

Outside pressure: P1,

The volume decrease from V2 to V1 ,

)( 211'1, VVpWe

1.3.1.5.2 Compress many times at the same pressure

1. Volume from V2 to V” by the pressure P” ;

2. Volume from V” to V’ by the pressure P’ ;

3. Volume from V’ to V1 by the pressure P1 .

)'()"'()"( 11'

2"'

2, VVpVVpVVpWe

1.3.1.5.3 Reversible compression

dVpWV

V ie 1

2

'3,

1

2

lnV

nRTV

'3,4, size,In ee WW

Both system and surrounding can get back to the original state.

1.3.1.6 Brief summary

1.3.2 Quasi-static process• Every moment in the process, system approaches

to the equilibrium state, so that, within the every little time dt, the state parameters of every system part have certain value, the whole process is considered to be composed by a serious of states which approach equilibrium states.

• Quasi-static process is an ideal process.

1.3.3 Reversible process

System changes from state (1) to (2) after some processes, if both the system and surrounding can go back to the origin state without leaving any perpetual changes. It is called as Reversible process.Otherwise, Irreversible process.

1.3.3 Reversible process

If the quasi-static expansion process don’t dissipate any energy, it can be regarded as a reversible process. During the process, every step approach to the equilibrium state, it can process adversely, from the initial state to the final, and then returns from the final state to the initial state,both the system and surround-ing can get back to the original state.

1.3.3.2 Characters of reversible process (1) During the state changing, the difference of the

impetus and the resistance is infinitesimal,system and surrounding are always approaching to the equilibrium state infinitely;

(2) After the system changing in a cycle, both the system and surrounding go back to the initial state, there is no dissipation during the changing.

(3) During the isothermal reversible process, system export the biggest work to surrounding, while surrounding export the lowest work to system.

1.3.4 Some process1.3.4.1 Isothermal process

During the change, the final temperature of the system is the same with the initial, and it equals to the surrounding temperature.

1.3.4.2 Isobaric process During the change, the final pressure of the

system is the same with the initial, and it equals to the surrounding pressure.

1.3.4.3 Isochoric process During the process, the system volume

keeps unchangeable.1.3.4.4 Adiabatic process During the change, no heat transfer

happens between system and surrounding. 1.3.4.5 Cyclic process The process of the system goes back

to the initial state after a series of changes.

1.4 Enthalpy In order to use conveniently, new state function is defined as follows:

)()( 1212 VVpUUQP )()( 1122 pVUpVU

12 HH = △H under the same pressure, the system does not do other work, the change of enthalpy equals to the isobaric thermal effect Qp.

pVUH VpQU p tconsIf p tan

1.5 Heat capacity

Specific heat capacity: The heat capacity of the substance which quality is 1g (or 1 Kg).

Its unit is or 1 1J K g 1 1J K kg

12 TT

QC

dQCT

1.5.1 Average heat capacity

1.5.2 Isobaric & isometric Heat capacity

Isobaric Cp: ( )d

pp p

Q HCTT

dp pH Q C T

( )d

VV V

Q UCTT

dV VU Q C T

Isometric Cv:

1.6 ApplicationGay-Lussac-Joule experiment

Ideal gas U and H

Ideal gas Cp-Cv

Adiabatic process

1.6.1 Gay-Lussac-Joule experiment In 1807, Gay-Lussac-Joule did the experiment

separately as following : Put two containers of the same capacity in the water- bath, fill the left ball with gas, the right ball is vacuum, the gas rush to the right one through the left one, and then it gets equilibrium.

1.6.1.2 Gay-Lussac-Joule experiment The temperature in the water-bath does not change, that is , Q=0, because the volume of the system is composed both of the balls, it does not export work in the system, W=0: according to the first law of thermo- dynamics,we can get ∆ U=0.

1.6.2 Ideal gas U and H

From the Gay-Lussac-Joule experiment, we can conclude that internal energy and enthalpy are temperature function.

( ) 0T

UV

( ) 0 TUp

( )U U T

( ) 0THV

( ) 0 T

Hp

( )H H T

Cv=f (T), Cp =f (T)

1.6.3 Ideal gas Cp-Cv

p VC C nR ,m ,mp VC C R

• In the isometric process, when the temperature ascends, all of the heat absorbed by the system is used to increase the thermodynamics energy. • But in the isobaric process, beside increasing U, the system needs to absorb more heat to do expansion work externally. • So, Cv<Cp

1.6.4 Adiabatic process

1.6.4.1 Work of adiabatic process

dU =Q -W =-W

• If the system exports work, the thermal energy decreases. • If the system get work, internal energy increases.

1.6.4.2 Equation of adiabatic process

1pV K

12TV K

13p T K

K1 K2 K3 are constants /p VC C

1.6.4.3 Calculation of adiabatic process(1) The work of the adiabatic reversible

process of ideal gas

2

1

dV

VW p V

2

1

= dV

V

KV

V ( )pV K

1 12 1

=1 1( )

(1 )K

V V

2 2 1 1=1

p V pVW

2 1( )1

nR T T

1 1 2 2p V p V K

1.6.4.4 Calculation of adiabatic process

(2) Work of adiabatic process

2

1

T

TCvdT C

v(T1-T2 )

because we do not introduce any other limitation conditions, this formula can be applied in adiabatic process of closed system which has fixed composing, need not always ideal gas, or reversible process.

W =- U

1.7 Real gas1.7.1 Joule-Thomson effect

Joule and Thomson designed a new experiment in 1852, which was called throttling process.

Analysis

• In Adiabatic contain, Q=0

• In the left, surrounding does Compress work.

• In the right, system does expand work

2 1U U U W

1 1W p V 1 1 1 1 ( =0 )pV V V V

2 2W p V 2 2 2 2 ( = 0 )p V V V V

1 2 1 1 2 2W W W p V p V i.e. 2 1 1 1 2 2U U p V p V

1.7.2 Enthalpy of real gases

• H2=H1

• H=constant

• But, U=f (T,V)

1.7.3 van der Waals equation

m2m

( )( )a

p V b RTV

a/ V2m in the formula is the emendation item of

pressure, internal pressure: b is the emendation item of volume occupied by gas molecule.

1.8 ThermochemistryReaction effect: After the reaction happens in the system, we

make the product temperature back to the initial state of the reaction, system discharges or absorbs energy.

Isobaric thermal effect:

Qp= ∆ H

Isometric thermal effect:

Qv= ∆ U

1.8.1 Isobaric & isometric thermal effect

Reactant

111 VpT

resultant 121 VpT

（ 3 ） 3r H(2)isometric

r 2 VU Q

2r H

1 1 2T p V

Product

pr QHisobaric 1 )1(

For Ideal gas,

3r2r1r HHH 3r22r )( HpVU

r 3

2

0, ( )HpV nRT

r rH U nRT

p VQ Q nRT

Therefore:

1.8.1.2 The relationship of Qp and Qv

p VQ Q nRT

rr H U nRT

∆n is the difference of the gas physical quantum of product and reactant.

Or

1.8.2 Equation of thermal chemistry

• The equation which denotes the relationship of chemistry reaction and thermal effect. • The substance phase, temperature, pressure,

composition should be indicated clearly. For the solid, crystal state should be indicated.

• e.g. 2 2H (g, ) I (g, ) 2HI(g, )p p p $ $ $

-1r m (298.15 K) -51.8 kJ molH $

1.8.2.2 Equation of thermochemistry

• ∆ stands for the change of H• $ stands for the product and reactant in

standard state • r stands for reaction• m stands for 1 mol• K stands for reaction temperature

r m (298.15 K)H $

1.8.3 Standard state of pressure

We have different regulation of the standard state of pressure, along with the subject process.

The initial is: 1 atm, 760 mmHg In 1985 it was regulated by GB: 101.325 kPa In 1993 it was regulated by GB: 1×105 .

1.8.3.2 Standard state of pressure The standard state of gas, the hypothesis

state : the ideal gas at p$. The standard state of solid and liquid: the

pure solid or liquid at p$ . There is no regulation on temperature

standard state, and the material has its own standard state at every temperature.

Usually we can check out the standard data of 298.15K in the table.

1.8.4 Distribution principle

21 2x xm v

2 x

kTv

m

1

2x kT So,

According to theory of gas molecular movement

•Molecular movement can be thought as 3 directions movement (x, y, z).•In x direction, movement energy

1.8.4.2 Distribution principle of single atom molecular 1

21

2

y

z

kT

kT

The same

3 + + 2x y zt kT

General translation movement energy:

经典热力学中，把每一个方向上的平均能量称为一个平方项，也称为一个自由度。所以能量是均匀地分配在每一个自由度上，这就是经典的能量均分原理。

1.9 Hess’s law• The thermal effect is only related with the initial

state and final state, it has nothing to do with the reaction way, regardless of how many steps the reaction is composed of.

• For example, (1) C(s) + O2(g)=CO2 (g) ∆rH$

m,1

(2) CO(g) + ½O2 (g)=CO2 (g) ∆rH$m,2

So, (1)-(2) to form (3)

(3) C(s) + ½O2 (g)=CO (g) ∆rH$m,3

m,2rm,1rm,3r HHH

1.10 Several thermal effect 1.10.1 standard molar enthalpy of formation Under the standard pressure, reaction

temperature, the change of enthalpy of 1 mol substance of standard state which synthesized by the most steady single substance is called standard molar enthalpy of formation.

∆fH$m (substance, phase, temperature)

1.10.1.2 formation enthalpy of compound

298.15K

-1mf (HCl,g,298.15 K) -92.31 kJ molH $

-1r m (298.15 K) -92.31 kJ molH $

2 21 12 2H (g, ) Cl (g, ) HCl(g, )p p p $ $ $

This is the standard molar enthalpy of HCl (g):

The H of the reaction is:

1.10.1.3 Application of formation enthalpy Under the standard pressure and reaction

temperature (usually 298.15K)

3DCEA2

r m f m f m f m f m(C) 3 (D) 2 (A) (E)H H H H H $ $ $ $ $

B f mB

(B)H $

ν is coefficient in the chemical equation, As for reactant is negative, product is positive.

1.10.2 Standard molar enthalpy of combustion• ∆cH$

m (substance, phase, T). “c” : combustion. • At standard pressure and certain reaction T, 1

mole organic substance discharges heat when it is oxidized to the appointed product, which is called ∆cH$

m.

g)(COC 2 O(l)HH 2

g)(SOS 2 g)(NN 2

HCl(aq)Cl

1.10.2.2 Example of combustion enthalpy Under 298.15K and standard pressure:

O(l)2Hg)(2COg)(2OCOOH(l)CH 2223 -1

r m 870.3 kJ molH $

-1c m 3(CH COOH,l,298.15 K) -870.3 kJ molH $

According to the definition, the standard molar enthalpy of combustion of the appointed product CO2 (g), H2O(l) is zero.

So

1.10.2.3 Calculating reaction heat The change of enthalpy of chemical

reaction is equal to the combustion enthalpy summation of the whole reactant subtracting that of product.

r m B c m

B

(298.15 K) - (B,298.15 K)H H $ $

R P

F

1.10.2.3.2 Example

Under 298.15K and standard pressure:

l)(O2Hs)()(COOCHOH(l)2CHs)(COOH)( 22332 （ A ） （ B ） （ C ） (D)

r m c m c m c m(A) 2 (B) - (C)H H H H $ $ $ $

so

• We can work out the formation enthalpy of organics which can not synthesize directly by the single substance.

• Under 298.15K and standard pressureOH(l)CHg)(Og)(2HC(s) 322 2

1

1.10.2.4 Calculating formation enthalpy

f m 3 c m c m 2(CH OH,l) (C,s) 2 (H ,g)H H H $ $ $

c m 3- (CH OH,l)H $

1.11 Kirchoff law• When the range of reaction temp. is wide

enough, the change of enthalpy is different, though the chemical reaction takes place at the same pressure.

• In 1858, Kirchoff brought forward Kirchoff Law.

pp

CT

H

B ,mB

(B)p pC C

dTCTHTH pTTmrmr

1212

True or false?

(a) A closed system cannot interact with its surroundings.

(b) Density is an intensive property.

(c) The Atlantic Ocean is an open system.

2.6 True or false?

(a) The quantities H, U, PV, △H, and P△V all have the same dimensions.

(b) △H is defined only for a constant-pressure process.

(c) For a constant-volume process in a closed system, △H =△U.

(a) Cp is a state function.

(b) Cp is an extensive property.

2.13 True or false?

(a) △H is a state function. (b) Cv is independent of T for every perfect gas.

(c) △U = q + w for every thermodynamic system at rest in the absence of external fields.

(d) A process in which the final temperature equals the initial temperature must be an isothermal process.

(e) For a closed system at rest in the absence of external fields, U = q +w.

(f) U remains constant in every isothermal process in a closed system.

(g) q = 0 for every cyclic process. (h) △U = 0 for every cyclic system. (i)△T = 0 for every adiabatic process in a

closed system.

(k) P-V work is usually negligible for solids and liquids.

(l) If neither heat nor matter can enter or leave a system, that system must be isolated.

Exercises

• P87-2, 3,4• P88-10• P89-4

Exercises

• P90-8, 9,10, 11• P91-13• P92- 22,• P93-26,33