第3章 理想气体的性质与热力过程

notes
（1）The behavior of real gas: high temperature, low pressure, low density (high specific volume), far from a state of condensation ------ treated as an ideal gas.
3-1-2 Ideal-Gas Equation of State （理想气体状态方程式） 1. Ideal-Gas Equation of State
For Ideal-Gas 1kg: pv = RgT For Ideal-Gas mkg: pV = mRgT
notes
（1）Clapeyron’s equation (In 1834) （2）At any equilibrium state: the p-v-T behavior of ideal-gas （3）Where: p—absolute pressure T— Kelvin temperature Rg—The gas constant
The Ideal-Gas Equation of State c，cv，cp，u，h，s of Ideal-Gas Ideal-Gas Processes （Four Basic Processes, Polytropic Processes)

3-1 The Ideal-Gas Equation of State
N2, H2, O2, CO2, CO
（2）The behavior of real gas: low temperature, high pressure, high density (low specific volume), not far from a state of condensation ------ treated as a real gas.
c a0 a1T a2T 2 a3T 3
Heat
q cdT (a0 a1T a2T 2 a3T 3 )dT
T1 T1
T2
T2
So Specific heat at constant pressure cp
c p a0 a1T a2T 2 a3T 3
41.8kJ
2. C, c, Cm, CV
（1）Specific heat（比热容） （2）Molar heat（摩尔热容）
c
q
dT
kJ /(kg K )
Cm Mc kJ /(mol K )
22.4
（3）Volume Heat（体积热容） CV Cm kJ /(m3 K )
Relationship among C，c，Cm，CV
cV
qV
dT
(
q
dT
)V c p
qp
dT
(
q
dT
)p
2. Specific Heats cv, cp in Reversible Processes q du p dv
q dh v dp
How to express du, dh?
For constant volume
For ideal gas, the specific heats cv, cp depend on temperature only.
cV f (T ) c p f (T )
4. Specific-Heat Relations of Ideal Gases （理想气体的 cv 和 cp 的关系） （1）迈耶公式：
说明
标准状态下， 0 101325 , T0 273.15K p Pa
简单求解过程：
解：按理想气体状态方程式， p1V1 p0V0
T1 T0
可得：
P0T1 V1 V0 P1T0
其中： 1 p
pb pg1 101325 20000 121325 Pa
故实际的送风量：
（理想气体状态方程式）
3-1-1 Ideal-Gas
1. Real Gas（实际气体）
• •
can’t neglect the volume of molecules there are attraction among molecule of real gas
2. Ideal-Gas（理想气体）
An Ideal gas is an imaginary substance that obeys these conditions: • The molecules of ideal-gas have no volume • There are no attraction among molecules of ideal-gas
Specific heat at constant volume cv
cV a0 a1T a2T 2 a3T 3
Heat transferred in a constant pressure process
q p c p dT
T1
T2
Heat transferred in a constant volume process
Steam power plants---water vapor Refrigerator--- ammonia, freon
（3）Water Vapor an Ideal Gas? • Water vapor exists in the air • Working substance in the steam power plant
1. Specific heat at constant volume cv: The energy required
to raise the temperature of the unit mass of a substance by one degree as the volume is maintained constant.
2. Alternative Forms of the Ideal-Gas Equation of State (不同物量的理想气体状态方程式)
• 1kg: p v = Rg T • mkg: pV = m Rg T • 1mol: P Vm = R T • nmol: p V = n R T
notes Rg-- gas constant 气体常数 R-- universal gas constant 通用气体常数
思考 题
Specific heats cp, cv, cp-cv, cp/cv depend on substance or state?
How to determine heat transferred by virtue of specific heats? (利用比热容，如何求解热量?)
c
For ideal gas
u f (T , v) f (T ) h u pv u RgT f (T )
u du cV ( )V T dT h dh cp ( ) p T dT
notes
Condition
Any process for ideal-gas Constant volume process for real gas Constant pressure process for real gas
C mc nCm V0CV
3. Influence Factors
（1）Substances （2）Thermal processes （3）Temperature
3-2-2 The Specific Heat at Constant Volume and at Constant Pressure（比定容热容和比定压热容）
1. Heat Capacity：
The energy required to raise the temperature of substance by one degree. Denoted by C, unit J/K.
C
Q
dT

Q
dt
1kg Water 20º C--30º C
1kg Iron 20º C--30º C 4.5kJ
R 8.314 J /(m ol K ) R Rg J /(kg K ) M
例
题
理想气体状态方程式的应用 某蒸汽锅炉燃煤需要的标准状况下，空气量 为 qV=66000m3/h，若鼓风炉送入的热空气温度为 t1=250°C，表压力 pg1=20.0kpa。当时当地的大气 压力 pb=101.325kpa。求实际的送风量为多少？
c p cV Rg C p ,m CV ,m R
Analysi s
How to obtain ? Why cp > cv at the same temperature?
（2）Specific heat ratio （比热容比）
ຫໍສະໝຸດ Baidu
cp cV
cp
1
Rg
1 cV Rg 1
qV cV dT
T1
T2
2. The average specific heats（平均比热容）
Thermodynamics
--- Chapter 3
The Properties of Ideal-Gas and Ideal-Gas Processes ---
Chapter 3 The Properties of Ideal-Gas and Ideal-Gas Processes
Contents
cV (
q
dT
)V (
du pdv u )( )V dT T
For constant pressure
dh vdp h cp ( )p ( )( )p dT dT T
q
Condition
Reversible Processes Any Substance
u cV ( )V T
利用比热容，如何求解热量？
c
q
dT

q
dt
q cdT cdt
q

T2
T1
cdT

t2
t1
cdt
3-2-3 The calculation of Heat
（利用理想气体的比热容计算热量）
1. The real specific heat capacity（真实比热容）
The specific heat in the state of instantaneous temperature.
V1 66000 101325 ( 273 250) 105543 3 / h m 121325 273.15
3-2 Specific Heat, Internal Energy, Enthalpy and Entropy of Ideal-Gas （理想气体的热容，热力学能，焓和熵） 3-2-1 Heat Capacity（热容的定义）
q
dT

q
dt
q cdT cdt
q cdT cdt
T1 t1 T2 t2
思考 题

cp cV

cV Rg cV
1
Rg cV
cp，cv，cp-cv，cp/cv与物质的种类是否有关？ 与气体的状态是否有关？ 解： cp，cv：与物质的种类和状态都有关系；
cp- cv= Rg ：与物质的种类有关，与状态无关； cp/cv =γ：与物质的种类和状态都有关系。
Specific heat at constant pressure cp: The energy required
to raise the temperature of the unit mass of a substance by one degree as the pressure is maintained constant.
= the change in internal energy with temperature at constant volume
h cp ( ) p T
= the change in enthalpy with temperature at constant pressure
3. Specific Heats cv, cp of Ideal-Gases（理想气体的cv, cp ）