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物理化学电子教案 —第二章（上）
U Q W? ? ?
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Chapter 2 The Thermodynamic First Law
2.1 Preface to the thermodynamics
2.2 The thermodynamic first law
2.3 Quasi-static process and reversible
process
2.4 Enthalpy
2.5 Heat capacity
2.6 The first law in ideal gases
2.7 Thermochemistry
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Contents
2.8 The Hess’s law
2.9 Heat in some processes
2.10 The temperature dependence of
the reaction enthalpy
—— Kirchhoff’s law
2.11 An adiabatic reaction
——non-isothermal reaction
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Thermodynamics
is the mathematical study of heat and
its relationship with mechanical energy
and other forms of work,
In chemical systems,it allows determination
of the feasibility,direction,and
equilibrium position of reactions.
Thermodynamics studies the transformations energy.
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Methods and limitations of thermodynamics
Thermodynamics
Limitation not with the microscopic
structure of matter,
is concerned only with the average characteristics
of large aggregations of molecules,not with the
characteristics of individual molecules.
In other words,classical thermodynamics takes
the macroscopic point of view and deals with
macroscopic phenomena.
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System and surroundings
The collection of matter thus specified
is called a thermodynamic system,
and everything external to the system
that has relation with the system
is called the surroundings or
the environment.
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Sorting out systems
Based on the relation of sys,and surr,
systems are defined as：
（ 1） open system
Matter exchange
Energy transfer
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System often encountered
（ 2） closed system
No matter
exchange
Energy transfer
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The big isolated system
（ 3） isolated system
No matter exchange,no Energy transfer.Sometimes
take into account the system and surroundings which has
relation with the system as a big isolated system.
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Another statement
When matter can be transferred between the
system and its surroundings we call it
an open system; when such transfer
is not possible the system is closed.
An isolated system is a closed system with
neither mechanical nor thermal contact
with its surroundings.
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The properties of system
A property of a system is any quantity or
characteristic that depends upon the state of the
system, Thermodynamic properties may be
classified as
extensive properties or volumetric properties，
whose value for the entire system is equal to the
sum of its values for all parts of the system.
intensive properties
are independent of the amount of substance in the
system.
Vm =V/n? Molar volume
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A state of thermodynamic equilibrium
If all the conditions for mechanical,
thermal,chemical,and electrical
equilibrium are satisfied,
the system is said to be
in a state of thermodynamic equilibrium
or simply in an equilibrium state.
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State function
When any property of a system changes there
is a change of state,and the system is said to
undergo a process,
A process whose initial and final states are
identical is called a cycle.
A property of a system depends only on the state of
the system and not on how that state was attained,
The uniqueness in the value of a property at a state
introduces the name state or point function for a
property.
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A path function,In contrast
quantities that depend on
the path of the process by
which a system changes
between two states
are called path
functions.
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An exact differential
Because a property is a point function,its
differential must be an exact or perfect or total
differential in mathematical term.
The line integral of the differential of a
property is independent of the path or curve
connecting the end states,and in the special
case of a complete cycle this integral vanishes.
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What is heat?
As a convention of sign,heat transferred to a
system is considered positive and heat transferred
from a system is considered negative.
The symbol Q is used to represent heat.
When the energy changes as a result of a
temperature difference between the system
and its surroundings we say that there
has been a flow of heat,
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What is work?
Work is energy in the form of orderly
motion,which may,in principle,be
harnessed so as to raise a weight.
The most common forms of work are
pressure-volume work and electrical work.
In mechanics,work is defined as the product
of a force and the displacement when both are
measured in the same direction.
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The P-V work
δW = - F dl = - Pex S dl = - Pex dV
Pex is the external pressure.
Work done by a system is considered
negative and
work done on a system is considered
positive.
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Explain, the path function
is a thermodynamic property
whose value depends upon the path
by which the transition from
the initial state to
the final state
takes place.Q and W
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The first law of thermodynamics
First kind of perpetual motion machine No way!
is essentially the law of conservation of energy
applied to thermodynamic system.
The energy of an isolated system is constant.
Through his famous experiments in 1843
Joule was led to the postulate that
heat and work were equivalent quantities.
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Thermodynamic Energy
When a system is carried through a
cycle,the first law is expressed by
? ? ???? 0QW
where both work and heat are
measured in the same units,
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Equation may be rewritten as
? ? 0?? ??? QW
It follows that since the cyclic integral of
the quantity (?Q+?w) is always zero,
this quantity must be the differential of a
property of the system,The state
function is the U – thermodynamic energy
Or internal energy.
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The change of thermodynamic energy
U1 U2
→→→→
↓ ↓
W Q
U2 = U1 + W + Q
U2 - U1 = W + Q WQU ???
The symbol △ will always be used to mean
―final-minus-initial‖.
This is the mathematical expression of the First Law.
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The important step in the development
involves switching attention to
infinitesimal transfers of heat and work,
we shall soon see how this opens up
powerful methods of calculation.
Let the work done on a system be the
infinitesimal amount dW and the heat
added be the infinitesimal amount dQ,
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Then in place of
which is appropriate when the transfers
are measurable,in the case of
infinitesimal changes
the thermodynamic energy of
the system changes by the amount dU,
where
dU = dQ + dW.
QWU ???
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ideal gas undergo:
1,Free expansion into vacuum.
If Pe = 0 it follows that the gas does no
work
on expansion—the piston has nothing to push
against,
δW = 0 for each step therefore W = 0.
δW = - Pex dV
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2,Expansion against constant pressure.
? ? ??????? VfVi VfVi ViVfP e xdVP e xP e x d VW ).(
Therefore the work done on the
system is
VP e xW ???
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Work and Process
W = - P2 ( V2 - V1 )
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Work and Process
e,3 1'( ' )W p V V? ? ?
3.three times expansion against const,pressure
" ( " ')p V V??
22( " )p V V??
(2)against const,P``,volume change from V`to V`` ;
(3)against const,Pf,volume change from V ``to Vf;
(1)against const,P`,volume change from V1 to V` ;
Conclusion?
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Many times - expansion
P` - P prime
P``- P double
prime
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Quasi-static expansion
4,Pex = Pin ± dp external,internal
e,4 e dW p V?? ?
2
1
i d
V
V
pV?? ?
一杯水，水不断蒸发，这样的膨胀过程是无限缓
慢的，每一步都接近于平衡态。所作的功为：
i( d ) dp p V? ? ??
1
2
ln Vn R T V?2
1
dV
V
n R T V
V?? ?
这种过程近似地可看作可逆过程，所作的功最大。
pg T
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Reversible expansion
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Compression process
1.一次等外压压缩
'
,1 1 1 2()eW p V V? ? ?
在外压为 下，一次从 压
缩到,环境对系统所作的功
（即系统得到的功）为：
1p 2V
1V
将体积从 压缩到,有如下三种途径,1V2V
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功与过程
2.多次等外压压缩
第一步：用 的压力将系统从 压缩到 ；
2V"p "V
第二步：用 的压力将系统从 压缩到 ；'V'p "V
第三步：用 的压力将系统从 压缩到 。
1p 1V'V
' " ",1 2( ) eW p V V? ? ?
整个过程所作的功为三步加和。
'11()p V V??
' ' " ( )p V V??
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功与过程
1
2
'
,3 d
V
ei VW p V?? ?
3.reversible compression
如果将蒸发掉的水气慢慢在杯中凝聚，使压力缓
慢增加，恢复到原状，所作的功为：
则系统和环境都能恢
复到原状。
2
1
ln Vn R T
V
?
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功与过程
从以上的膨胀与压缩过程看出，功与变化的途
径有关。虽然始终态相同，但途径不同，所作的功
也大不相同。显然,可逆膨胀，系统对环境作最大
功； 可逆压缩，环境对系统作最小功。
功与过程
小结：
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Quasi-static Process
在过程进行的每一瞬间，系统都接近于平衡状
态，以致在任意选取的短时间 dt内，状态参量在整
个系统的各部分都有确定的值，整个过程可以看成
是 由一系列极接近平衡的状态所构成,这种过程称
为准静态过程。
准静态过程是一种理想过程，实际上是办不到
的。上例无限缓慢地压缩和无限缓慢地膨 胀 过程可
近似看作为准静态过程。
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Reversible process
A system is said to have undergone a
reversible process,if at the conclusion of the
process,the initial states of the system and
the surroundings can be restored without
leaving any net change at all elsewhere.
If when the system and the surroundings are
restored to their respective initial states there
are net changes left elsewhere,the process is
said to be irreversible.
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Reversible process
可逆过程的特点：
（ 1）状态变化时推动力与阻力相差无限小，系统
与环境始终无限接近于平衡态；
（ 3）系统变化一个循环后，系统和环境均恢复原态，
变化过程中无任何耗散效应；
（ 4）等温可逆过程中，系统对环境作最大功，环境
对系统作最小功。
（ 2）过程中的任何一个中间态都可以从正、逆两个
方向到达；
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A system is said to have undergone
A gas confined in a cylinder with a well-lubricated
piston can be made to undergo an approximately
reversible process by pushing or pulling the piston
in slow motion or by dividing the process into very
small steps.
A reversible process as follows:
This is true because in the limit in any stage of the
process it could be turned into the opposite
direction by an infinitesimal change of the external
conditions,
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常见的变化过程
（ 1） isothermal process
系统的始态温度与终态温度相同，并等于环
境温度。
（ 2） isobaric process
系统的始态压力与终态压力相同，并等于环
境压力。
（ 3） isochoric process
系统的容积始终保持不变。
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常见的变化过程
（ 4） adiabatic process
系统与环境不发生热的传递,对那些变化极
快的过程，如爆炸，快速燃烧，系统与环境来不
及发生热交换，那个瞬间可近似作为绝热过程处
理。
（ 5） cyclic process
系统从始态出发，经过一系列变化后又回到
了始态的变化过程。在这个过程中，所有状
态函数的变量等于零。
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The constant-volume heat
WQU V ???
W = 0
QU V??
(Const,n,V; W` = 0)
The constant-volume heat
is equal to the increment of
the thermodynamic energy.
(W` implies work other than p-V work)
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The constant-pressure heat
)( 12 VVPQWQU PP ??????
(Const,n,P; W’ = 0)
The constant-pressure heat is equal
to the increment of the enthalpy.
VPVPQU P 1122 ????
VPUQVPU P 111222 ????
HQH P 12 ??
QH P??
H = U + PVDefine:
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Enthalpy
definition,H = U + pV
焓不是能量 虽然具有能量的单位，但不遵守能量
守恒定律。
焓是状态函数 定义式中焓由状态函数组成。
为什么要定义焓？
为了使用方便, 因为在等压, 不作非膨胀功的条
件下, 焓变等于等压热, 易测量,
从而可求其它热力学函数的变化值 。p
Q pQ
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Heat capacity
d
QC
T
?? (变化率 )
Heat
capacity:
For an infinitesimal transfer of heat the
increase in temperature is proportional
to the amount of heat supplied,and so
dQ = CdT.
Cm = C/n
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Molar heat capacity
Specific heat capacity：
11J K g???? 11J K k g????
单位重量的,物质的 热容。
单位物质的量的、物质的 热容。
Molar heat capacity Cm：
单位为,。
11J K m o l????
单位为：
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Molar heat capacity
()d pppQ HC TT? ??? ?
dppH Q C T? ? ? ?
At const,
pressure
Cp：
()d VVVQ UC TT? ??? ?
dVVU Q C T? ? ? ?
At const.
volume
Cv：
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How to calculate the heat?
The heat capacities at constant volume and
constant pressure are both special cases of the
general definition in eqn dQ = C dT,
This means that both may be defined by adding a
label denoting the constraint:
dQv = CvdT,at constant volume,no work.
dQp = CpdT,at constant pressure,
no work other than pV-work.
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热容与温度的函数关系因物
质、物态和温度区间的不同而有不同的形式。例如，
气体的等压摩尔热容与 T 的关系有如下经验式：
The constant-pressure molar heat capacity
热容与温度的关系：
2,mpC a bT c T? ? ? ? ???
2,m '/pC a b T c T? ? ? ? ???
或
式中 a,b,c,c’,..,是经验常数，由各种物质本身的
特性决定，可从热力学数据表中查找。
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Gay-Lussac - Joule experiment
盖 ?吕萨克 1807年，焦耳在 1843年分别做了如下实验：
They used two vessels immersed
in a water bath,One vessel was
filled with air at 22 atm,the other
was evacuated.
The air was allowed to expand
into a vacuum,
dT=0,Q=0,W=0,
then dU=0
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The thermodynamic implication of
△ U = W + Q = 0
U = f ( P,T )
0??
?
??
?
?
?
??
?
?
??
?
?
?
?? dT
T
UdP
P
UdU
PT
dT = 0,
dP ≠ 0
0,0 ?? ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
V
U
P
U
TT
the experiment is as
follows.
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U and H for perfect gas
从盖 ?吕萨克 —焦耳实验得到 理想气体的热力
学能和焓仅是温度的函数,用数学表示为：
( ) 0TUV? ??
( ) 0THV? ??
()U U T?
()H H T?
即,在恒温时，改变体积或压力，理想气体的热
力学能和焓保持不变。 还可以推广为理想气体的
Cv,Cp也仅为温度的函数。
( ) 0 TUp? ??
( ) 0 THp? ??
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The relation between Cp and Cv
气体的 Cp恒大于 Cv。 in the case of a pg：
因为等容过程中，升高温度，系统所吸的
热全部用来增加热力学能；而等压过程中，所
吸的热除增加热力学能外，还要多吸一点热量
用来对外做膨胀功，所以 气体的 Cp恒大于 Cv 。
p VC C n R??
,m,mp VC C R??
monatomic pg,(3/2)R,
diatomic pg, (5/2)R
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一般封闭系统 Cp与 Cv之差
( ) ( )ppVVHUCC TT??? ? ?
()( ) ( )
p V
U P V U H
TT
?? ???
?? （代入 定义式）
( ) ( ) ( )pp VU V UpT T T? ? ?? ? ?? ? ?
( ) ( ) ( ) ( )ppVTU U U VT T V T? ? ? ???? ? ? ?
根据复合函数的偏微商公式（见下页）
代入上式，得：
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一般封闭系统 Cp与 Cv之差
( ) ( ) ( )p p p pV U V VC C pV T T? ? ?? ? ?? ? ?
[ ( ) ] ( )ppUVp VT???? ??
对理想气体，
( ) 0,pUV? ??
所以
p VC C nR??
( ) /pV n R pT? ??
H = U +pV,dH = dU +d(pV)=dU +nRdT
CpdT = CvdT +nRdT
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一般封闭系统 Cp与 Cv之差
d ( ) d ( ) dVTUUU T VTV????
证明：
( ) ( ) ( ) ( )ppVTU U U VT T V T? ? ? ???? ? ? ?
d ( ) d ( ) [ ( ) d ( ) d ]pV T TU U V VU T T pT V T p? ? ? ?? ? ?? ? ? ?
代入 表达式得：dV
设,(,),(,)U U T V V V T p??
d ( ) d ( ) dp TVVV T pTp????
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一般封闭系统 Cp与 Cv之差
d ( ) d ( ) dTpUUU p TpT????
重排，将 项分开，得：d,dpT
d ( ) ( ) d [ ( ) ( ) ( ) ] dT T V T pU V U U VU p TV p T V T? ? ? ? ?? ? ?? ? ? ? ?
对照 的两种表达式，得：dU
因为 也是 的函数，
,TpU (,)U U T p?
( ) ( ) ( ) ( )p V T pU U U VT T V T? ? ? ???? ? ? ?
= ( ) d [ ( ) ( ) ( ) ] dT V T pU U U VpTp T V T? ? ? ???? ? ? ?
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Adiabatic process
绝热过程的功
d U Q W? ? ? ?
在绝热过程中，系统与环境间无热的交换，但可
以有功的交换。根据热力学第一定律：
这时，若系统对外作功，热力学能下降，系统温
度必然降低，反之，则系统温度升高。因此绝热压缩，
使系统温度升高，而 绝热膨胀，可获得低温 。
= 0WQ? ? ?（因为 ）
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Calculate the work done
in an adiabatic expansion.
WdU ??
pg; r.
P d VdTCn mV ??,
V
n R T d V??
0lnln,?? VRdTdC mV
1
,
,,
,
???? ?
C
CC
C
R
mV
mVmP
mV
0lnln 1 ?? ?VdTd ?
? ? 0.ln 1 ??VTd ?
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Adiabatic process
Equation of adiabatic reversible of ideal gas:
1 3p T K??? ?
eqns,1 2 3,,K K K /p VCC? ?
1p V K? ?
1 2T V K? ? ?
Ratio of heat capacity
Pg,a,r,
↑
All are constants↑
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Chapter 0 Introduction
Physical chemistry
is an unexpected shock to many
university students,
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From the Semi-empirical approaches
of the school laboratory,
first year undergraduates suddenly
find themselves
propelled into
an unexpected quagmire of
definitions and equations,
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applicability
Worse still,although the applicability
of the subject
is sometimes obvious,studying the
behavior of a particle in an infinitely
deep well
can seem nothing short of farcical on
first approach.
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As the authors of this text,
we therefore found ourselves
in a paradoxical situation –
writing a book containing
lists of facts on a subject
which isn’t primarily
about lists of facts,
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So although
this book
is primarily a revision text
we did not wish
it to be merely an encyclopedia
of equations and definitions,
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In order that
the conceptual content of the book
is given sufficient weight
to aid understanding,
we have limited
the extent of the mathematical treatments
to the minimum
required of a student,
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The rigorous arguments
which underpin much of physical
chemistry
are left for other authors
to tackle,
with our own recommendations
for further reading
included in the bibliography,
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Since our primary aim
has been to produce a quick reference and
revision text for
all first and second year degree students
whose studies include physical chemistry,
we have recognized that
different aspects of the subject are useful
in different fields of study,
The end
物理化学电子教案 —第二章（上）
U Q W? ? ?
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Chapter 2 The Thermodynamic First Law
2.1 Preface to the thermodynamics
2.2 The thermodynamic first law
2.3 Quasi-static process and reversible
process
2.4 Enthalpy
2.5 Heat capacity
2.6 The first law in ideal gases
2.7 Thermochemistry
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Contents
2.8 The Hess’s law
2.9 Heat in some processes
2.10 The temperature dependence of
the reaction enthalpy
—— Kirchhoff’s law
2.11 An adiabatic reaction
——non-isothermal reaction
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Thermodynamics
is the mathematical study of heat and
its relationship with mechanical energy
and other forms of work,
In chemical systems,it allows determination
of the feasibility,direction,and
equilibrium position of reactions.
Thermodynamics studies the transformations energy.
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Methods and limitations of thermodynamics
Thermodynamics
Limitation not with the microscopic
structure of matter,
is concerned only with the average characteristics
of large aggregations of molecules,not with the
characteristics of individual molecules.
In other words,classical thermodynamics takes
the macroscopic point of view and deals with
macroscopic phenomena.
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System and surroundings
The collection of matter thus specified
is called a thermodynamic system,
and everything external to the system
that has relation with the system
is called the surroundings or
the environment.
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Sorting out systems
Based on the relation of sys,and surr,
systems are defined as：
（ 1） open system
Matter exchange
Energy transfer
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System often encountered
（ 2） closed system
No matter
exchange
Energy transfer
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The big isolated system
（ 3） isolated system
No matter exchange,no Energy transfer.Sometimes
take into account the system and surroundings which has
relation with the system as a big isolated system.
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Another statement
When matter can be transferred between the
system and its surroundings we call it
an open system; when such transfer
is not possible the system is closed.
An isolated system is a closed system with
neither mechanical nor thermal contact
with its surroundings.
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The properties of system
A property of a system is any quantity or
characteristic that depends upon the state of the
system, Thermodynamic properties may be
classified as
extensive properties or volumetric properties，
whose value for the entire system is equal to the
sum of its values for all parts of the system.
intensive properties
are independent of the amount of substance in the
system.
Vm =V/n? Molar volume
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A state of thermodynamic equilibrium
If all the conditions for mechanical,
thermal,chemical,and electrical
equilibrium are satisfied,
the system is said to be
in a state of thermodynamic equilibrium
or simply in an equilibrium state.
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State function
When any property of a system changes there
is a change of state,and the system is said to
undergo a process,
A process whose initial and final states are
identical is called a cycle.
A property of a system depends only on the state of
the system and not on how that state was attained,
The uniqueness in the value of a property at a state
introduces the name state or point function for a
property.
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A path function,In contrast
quantities that depend on
the path of the process by
which a system changes
between two states
are called path
functions.
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An exact differential
Because a property is a point function,its
differential must be an exact or perfect or total
differential in mathematical term.
The line integral of the differential of a
property is independent of the path or curve
connecting the end states,and in the special
case of a complete cycle this integral vanishes.
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What is heat?
As a convention of sign,heat transferred to a
system is considered positive and heat transferred
from a system is considered negative.
The symbol Q is used to represent heat.
When the energy changes as a result of a
temperature difference between the system
and its surroundings we say that there
has been a flow of heat,
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What is work?
Work is energy in the form of orderly
motion,which may,in principle,be
harnessed so as to raise a weight.
The most common forms of work are
pressure-volume work and electrical work.
In mechanics,work is defined as the product
of a force and the displacement when both are
measured in the same direction.
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The P-V work
δW = - F dl = - Pex S dl = - Pex dV
Pex is the external pressure.
Work done by a system is considered
negative and
work done on a system is considered
positive.
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Explain, the path function
is a thermodynamic property
whose value depends upon the path
by which the transition from
the initial state to
the final state
takes place.Q and W
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The first law of thermodynamics
First kind of perpetual motion machine No way!
is essentially the law of conservation of energy
applied to thermodynamic system.
The energy of an isolated system is constant.
Through his famous experiments in 1843
Joule was led to the postulate that
heat and work were equivalent quantities.
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Thermodynamic Energy
When a system is carried through a
cycle,the first law is expressed by
? ? ???? 0QW
where both work and heat are
measured in the same units,
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Equation may be rewritten as
? ? 0?? ??? QW
It follows that since the cyclic integral of
the quantity (?Q+?w) is always zero,
this quantity must be the differential of a
property of the system,The state
function is the U – thermodynamic energy
Or internal energy.
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The change of thermodynamic energy
U1 U2
→→→→
↓ ↓
W Q
U2 = U1 + W + Q
U2 - U1 = W + Q WQU ???
The symbol △ will always be used to mean
―final-minus-initial‖.
This is the mathematical expression of the First Law.
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The important step in the development
involves switching attention to
infinitesimal transfers of heat and work,
we shall soon see how this opens up
powerful methods of calculation.
Let the work done on a system be the
infinitesimal amount dW and the heat
added be the infinitesimal amount dQ,
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Then in place of
which is appropriate when the transfers
are measurable,in the case of
infinitesimal changes
the thermodynamic energy of
the system changes by the amount dU,
where
dU = dQ + dW.
QWU ???
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ideal gas undergo:
1,Free expansion into vacuum.
If Pe = 0 it follows that the gas does no
work
on expansion—the piston has nothing to push
against,
δW = 0 for each step therefore W = 0.
δW = - Pex dV
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2,Expansion against constant pressure.
? ? ??????? VfVi VfVi ViVfP e xdVP e xP e x d VW ).(
Therefore the work done on the
system is
VP e xW ???
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Work and Process
W = - P2 ( V2 - V1 )
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Work and Process
e,3 1'( ' )W p V V? ? ?
3.three times expansion against const,pressure
" ( " ')p V V??
22( " )p V V??
(2)against const,P``,volume change from V`to V`` ;
(3)against const,Pf,volume change from V ``to Vf;
(1)against const,P`,volume change from V1 to V` ;
Conclusion?
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Many times - expansion
P` - P prime
P``- P double
prime
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Quasi-static expansion
4,Pex = Pin ± dp external,internal
e,4 e dW p V?? ?
2
1
i d
V
V
pV?? ?
一杯水，水不断蒸发，这样的膨胀过程是无限缓
慢的，每一步都接近于平衡态。所作的功为：
i( d ) dp p V? ? ??
1
2
ln Vn R T V?2
1
dV
V
n R T V
V?? ?
这种过程近似地可看作可逆过程，所作的功最大。
pg T
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Reversible expansion
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Compression process
1.一次等外压压缩
'
,1 1 1 2()eW p V V? ? ?
在外压为 下，一次从 压
缩到,环境对系统所作的功
（即系统得到的功）为：
1p 2V
1V
将体积从 压缩到,有如下三种途径,1V2V
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功与过程
2.多次等外压压缩
第一步：用 的压力将系统从 压缩到 ；
2V"p "V
第二步：用 的压力将系统从 压缩到 ；'V'p "V
第三步：用 的压力将系统从 压缩到 。
1p 1V'V
' " ",1 2( ) eW p V V? ? ?
整个过程所作的功为三步加和。
'11()p V V??
' ' " ( )p V V??
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功与过程
1
2
'
,3 d
V
ei VW p V?? ?
3.reversible compression
如果将蒸发掉的水气慢慢在杯中凝聚，使压力缓
慢增加，恢复到原状，所作的功为：
则系统和环境都能恢
复到原状。
2
1
ln Vn R T
V
?
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功与过程
从以上的膨胀与压缩过程看出，功与变化的途
径有关。虽然始终态相同，但途径不同，所作的功
也大不相同。显然,可逆膨胀，系统对环境作最大
功； 可逆压缩，环境对系统作最小功。
功与过程
小结：
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Quasi-static Process
在过程进行的每一瞬间，系统都接近于平衡状
态，以致在任意选取的短时间 dt内，状态参量在整
个系统的各部分都有确定的值，整个过程可以看成
是 由一系列极接近平衡的状态所构成,这种过程称
为准静态过程。
准静态过程是一种理想过程，实际上是办不到
的。上例无限缓慢地压缩和无限缓慢地膨 胀 过程可
近似看作为准静态过程。
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Reversible process
A system is said to have undergone a
reversible process,if at the conclusion of the
process,the initial states of the system and
the surroundings can be restored without
leaving any net change at all elsewhere.
If when the system and the surroundings are
restored to their respective initial states there
are net changes left elsewhere,the process is
said to be irreversible.
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Reversible process
可逆过程的特点：
（ 1）状态变化时推动力与阻力相差无限小，系统
与环境始终无限接近于平衡态；
（ 3）系统变化一个循环后，系统和环境均恢复原态，
变化过程中无任何耗散效应；
（ 4）等温可逆过程中，系统对环境作最大功，环境
对系统作最小功。
（ 2）过程中的任何一个中间态都可以从正、逆两个
方向到达；
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A system is said to have undergone
A gas confined in a cylinder with a well-lubricated
piston can be made to undergo an approximately
reversible process by pushing or pulling the piston
in slow motion or by dividing the process into very
small steps.
A reversible process as follows:
This is true because in the limit in any stage of the
process it could be turned into the opposite
direction by an infinitesimal change of the external
conditions,
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常见的变化过程
（ 1） isothermal process
系统的始态温度与终态温度相同，并等于环
境温度。
（ 2） isobaric process
系统的始态压力与终态压力相同，并等于环
境压力。
（ 3） isochoric process
系统的容积始终保持不变。
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常见的变化过程
（ 4） adiabatic process
系统与环境不发生热的传递,对那些变化极
快的过程，如爆炸，快速燃烧，系统与环境来不
及发生热交换，那个瞬间可近似作为绝热过程处
理。
（ 5） cyclic process
系统从始态出发，经过一系列变化后又回到
了始态的变化过程。在这个过程中，所有状
态函数的变量等于零。
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The constant-volume heat
WQU V ???
W = 0
QU V??
(Const,n,V; W` = 0)
The constant-volume heat
is equal to the increment of
the thermodynamic energy.
(W` implies work other than p-V work)
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The constant-pressure heat
)( 12 VVPQWQU PP ??????
(Const,n,P; W’ = 0)
The constant-pressure heat is equal
to the increment of the enthalpy.
VPVPQU P 1122 ????
VPUQVPU P 111222 ????
HQH P 12 ??
QH P??
H = U + PVDefine:
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Enthalpy
definition,H = U + pV
焓不是能量 虽然具有能量的单位，但不遵守能量
守恒定律。
焓是状态函数 定义式中焓由状态函数组成。
为什么要定义焓？
为了使用方便, 因为在等压, 不作非膨胀功的条
件下, 焓变等于等压热, 易测量,
从而可求其它热力学函数的变化值 。p
Q pQ
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Heat capacity
d
QC
T
?? (变化率 )
Heat
capacity:
For an infinitesimal transfer of heat the
increase in temperature is proportional
to the amount of heat supplied,and so
dQ = CdT.
Cm = C/n
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Molar heat capacity
Specific heat capacity：
11J K g???? 11J K k g????
单位重量的,物质的 热容。
单位物质的量的、物质的 热容。
Molar heat capacity Cm：
单位为,。
11J K m o l????
单位为：
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Molar heat capacity
()d pppQ HC TT? ??? ?
dppH Q C T? ? ? ?
At const,
pressure
Cp：
()d VVVQ UC TT? ??? ?
dVVU Q C T? ? ? ?
At const.
volume
Cv：
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How to calculate the heat?
The heat capacities at constant volume and
constant pressure are both special cases of the
general definition in eqn dQ = C dT,
This means that both may be defined by adding a
label denoting the constraint:
dQv = CvdT,at constant volume,no work.
dQp = CpdT,at constant pressure,
no work other than pV-work.
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热容与温度的函数关系因物
质、物态和温度区间的不同而有不同的形式。例如，
气体的等压摩尔热容与 T 的关系有如下经验式：
The constant-pressure molar heat capacity
热容与温度的关系：
2,mpC a bT c T? ? ? ? ???
2,m '/pC a b T c T? ? ? ? ???
或
式中 a,b,c,c’,..,是经验常数，由各种物质本身的
特性决定，可从热力学数据表中查找。
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Gay-Lussac - Joule experiment
盖 ?吕萨克 1807年，焦耳在 1843年分别做了如下实验：
They used two vessels immersed
in a water bath,One vessel was
filled with air at 22 atm,the other
was evacuated.
The air was allowed to expand
into a vacuum,
dT=0,Q=0,W=0,
then dU=0
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The thermodynamic implication of
△ U = W + Q = 0
U = f ( P,T )
0??
?
??
?
?
?
??
?
?
??
?
?
?
?? dT
T
UdP
P
UdU
PT
dT = 0,
dP ≠ 0
0,0 ?? ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
V
U
P
U
TT
the experiment is as
follows.
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U and H for perfect gas
从盖 ?吕萨克 —焦耳实验得到 理想气体的热力
学能和焓仅是温度的函数,用数学表示为：
( ) 0TUV? ??
( ) 0THV? ??
()U U T?
()H H T?
即,在恒温时，改变体积或压力，理想气体的热
力学能和焓保持不变。 还可以推广为理想气体的
Cv,Cp也仅为温度的函数。
( ) 0 TUp? ??
( ) 0 THp? ??
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The relation between Cp and Cv
气体的 Cp恒大于 Cv。 in the case of a pg：
因为等容过程中，升高温度，系统所吸的
热全部用来增加热力学能；而等压过程中，所
吸的热除增加热力学能外，还要多吸一点热量
用来对外做膨胀功，所以 气体的 Cp恒大于 Cv 。
p VC C n R??
,m,mp VC C R??
monatomic pg,(3/2)R,
diatomic pg, (5/2)R
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一般封闭系统 Cp与 Cv之差
( ) ( )ppVVHUCC TT??? ? ?
()( ) ( )
p V
U P V U H
TT
?? ???
?? （代入 定义式）
( ) ( ) ( )pp VU V UpT T T? ? ?? ? ?? ? ?
( ) ( ) ( ) ( )ppVTU U U VT T V T? ? ? ???? ? ? ?
根据复合函数的偏微商公式（见下页）
代入上式，得：
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一般封闭系统 Cp与 Cv之差
( ) ( ) ( )p p p pV U V VC C pV T T? ? ?? ? ?? ? ?
[ ( ) ] ( )ppUVp VT???? ??
对理想气体，
( ) 0,pUV? ??
所以
p VC C nR??
( ) /pV n R pT? ??
H = U +pV,dH = dU +d(pV)=dU +nRdT
CpdT = CvdT +nRdT
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一般封闭系统 Cp与 Cv之差
d ( ) d ( ) dVTUUU T VTV????
证明：
( ) ( ) ( ) ( )ppVTU U U VT T V T? ? ? ???? ? ? ?
d ( ) d ( ) [ ( ) d ( ) d ]pV T TU U V VU T T pT V T p? ? ? ?? ? ?? ? ? ?
代入 表达式得：dV
设,(,),(,)U U T V V V T p??
d ( ) d ( ) dp TVVV T pTp????
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一般封闭系统 Cp与 Cv之差
d ( ) d ( ) dTpUUU p TpT????
重排，将 项分开，得：d,dpT
d ( ) ( ) d [ ( ) ( ) ( ) ] dT T V T pU V U U VU p TV p T V T? ? ? ? ?? ? ?? ? ? ? ?
对照 的两种表达式，得：dU
因为 也是 的函数，
,TpU (,)U U T p?
( ) ( ) ( ) ( )p V T pU U U VT T V T? ? ? ???? ? ? ?
= ( ) d [ ( ) ( ) ( ) ] dT V T pU U U VpTp T V T? ? ? ???? ? ? ?
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Adiabatic process
绝热过程的功
d U Q W? ? ? ?
在绝热过程中，系统与环境间无热的交换，但可
以有功的交换。根据热力学第一定律：
这时，若系统对外作功，热力学能下降，系统温
度必然降低，反之，则系统温度升高。因此绝热压缩，
使系统温度升高，而 绝热膨胀，可获得低温 。
= 0WQ? ? ?（因为 ）
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Calculate the work done
in an adiabatic expansion.
WdU ??
pg; r.
P d VdTCn mV ??,
V
n R T d V??
0lnln,?? VRdTdC mV
1
,
,,
,
???? ?
C
CC
C
R
mV
mVmP
mV
0lnln 1 ?? ?VdTd ?
? ? 0.ln 1 ??VTd ?
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Adiabatic process
Equation of adiabatic reversible of ideal gas:
1 3p T K??? ?
eqns,1 2 3,,K K K /p VCC? ?
1p V K? ?
1 2T V K? ? ?
Ratio of heat capacity
Pg,a,r,
↑
All are constants↑
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Chapter 0 Introduction
Physical chemistry
is an unexpected shock to many
university students,
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From the Semi-empirical approaches
of the school laboratory,
first year undergraduates suddenly
find themselves
propelled into
an unexpected quagmire of
definitions and equations,
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applicability
Worse still,although the applicability
of the subject
is sometimes obvious,studying the
behavior of a particle in an infinitely
deep well
can seem nothing short of farcical on
first approach.
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As the authors of this text,
we therefore found ourselves
in a paradoxical situation –
writing a book containing
lists of facts on a subject
which isn’t primarily
about lists of facts,
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So although
this book
is primarily a revision text
we did not wish
it to be merely an encyclopedia
of equations and definitions,
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In order that
the conceptual content of the book
is given sufficient weight
to aid understanding,
we have limited
the extent of the mathematical treatments
to the minimum
required of a student,
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The rigorous arguments
which underpin much of physical
chemistry
are left for other authors
to tackle,
with our own recommendations
for further reading
included in the bibliography,
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Since our primary aim
has been to produce a quick reference and
revision text for
all first and second year degree students
whose studies include physical chemistry,
we have recognized that
different aspects of the subject are useful
in different fields of study,
The end
