大连理工大学：《工程热力学》课程教学资源（PPT课件）3 气体与蒸汽的热力性质 Thermodynamic Property of Gas & Vapor

3 ThermodynamicProperty of Gas &VaporObjective·ldeal-Gas Equation of StateHeat Capacity, Specific Heat, Internal Energy &Enthalpy: Property of Ideal-Gas and Its Mixture·Real-Gas&Derivation from ldeal-Gas· Property Diagrams of Phase-Change process forPure SubstancesThermodynamic property of humidity air (moisture)1

1 3 Thermodynamic Property of Gas & Vapor Objective •Ideal-Gas Equation of State •Heat Capacity, Specific Heat, Internal Energy & Enthalpy • Property of Ideal-Gas and Its Mixture • Real-Gas & Derivation from Ideal-Gas • Property Diagrams of Phase-Change process for Pure Substances •Thermodynamic property of humidity air (moisture)

Ideal-Gas Equation of StateFrom a molecular standpoint, an ideal gas moleculeis a completely elastic, point particle (no volume)withno molecule-molecule interaction forcesECondition:GASIDEAIoto·lowpressure10MP30060.05MP·high temperature00MP:100PO10kP0.skPs200040.0100.1tmks100

2 Ideal-Gas Equation of State From a molecular standpoint, an ideal gas molecule is a completely elastic, point particle (no volume) with no molecule-molecule interaction forces. Condition: • low pressure • high temperature

Ideal-Gas Equation of StateAn equation of state is...- ...a mathematical expression that definesthe thermodynamic state of a substance andrelates volume, pressure, and temperatureThere are several equations of state. The ideal-gas equation is the simplest and best-known one.It predicts the P-v-T behavior of agas quiteaccurately within some properly selected region.3

3 Ideal-Gas Equation of State An equation of state is. – .a mathematical expression that defines the thermodynamic state of a substance and relates volume, pressure, and temperature. There are several equations of state. The ideal￾gas equation is the simplest and best-known one. It predicts the P-v-T behavior of a gas quite accurately within some properly selected region

Ideal-Gas Equation of Statep- Absolute Pressure, kPapV= RTv- Specific Volume, m"/kgT- Absolute Temperature, KpV = mRTV-Volume, m3pV = NR.TN - Mole Number, kmolmR, -Universal Gas ConstantR, = 8.314kJ/(kmol .K)R8.314R:kJ/(kg ·K)一MMM - Molar Mass4

4 Ideal-Gas Equation of State pV NR T pV mRT pv RT = m = = 3 3 ,kPa ,m /kg ,K , m ,kmol 8.314kJ/(kmol K) 8.314 kJ/(kg K) m m m p Absolute Pressure v Specific Volume T Absolute Temperature V Volume N Mole Number R Universal Gas Constant R R R M M M Molar Mass − − − − − − =  = =  −

2.鼓风机需要输运2900kg/h空气，输运时空气温度为30℃，其管道上压力表读数0.3MPa，当时当地大气压力为0.1MPa，求实际送风量(m3/h)为多少？解：根据理想气体状态方程pV =NR.Tm绝对压力p = 0.3+0.1=0.4MPaT =30+273.15 =303.15KNR.T:Vp2900×8.314×303.15= 630m3/h29×4005

5 2. 鼓风机需要输运2900kg/h空气，输运时空气温度为30℃，其管道上压力表 读数0.3MPa，当时当地大气压力为0.1MPa，求实际送风量(m3 /h)为多少？ 解：根据理想气体状态方程 m pV NR T = 0.3 0.1 0.4MPa 30 273.15 303.15K p T = + = = + = 2900 8.314 303.15 3 630m /h 29 400 NR Tm V p  =   = =  绝对压力

Heat Capacity, Specific HeatHeat Capacity-the energy required to raise the temperature of a substanceby one degree.Q(J/K)CdTSpecific HeatqkJ/(kg ·K)c=一perUnitmassdTSqMM ·c kJ/(kmol · K)-per Unit Mole=CmdTCmkJ/(m3 .K)-per Unit Volume22.46

6 Heat Capacity, Specific Heat Heat Capacity －the energy required to raise the temperature of a substance by one degree. (J/K) d δ T Q C = Specific Heat －per Unit mass kJ/(kg K) d δ =  T q c kJ/(kmol K) d δ =  = M c  T q －per Unit Mole c m M －per Unit Volume kJ/(m K) 22.4 ' 3 =  m c c

&c国C，一定容比热容1stlawq = du + pdy内能是 和T的函数，是状态参数d1alsqdTa1

7 v p c &c v c －定容比热容 1 st law δq u p v = + d d d ( ) d ( ) d v T u u u T v T v   = +   内能是 和 的函数，是状态参数 δ ( ) d v v q u c T T   = =  v T

&c-一定压比热容p1stlawSq = dh - vd恰是 P和T 的函数，是状态参数ahdTdhdpaTopoqahDdTaT8

8 v p c &c 1 st law δq h v p = − d d d ( ) d ( ) d p T h h h T p T p   = +   焓是 和 的函数，是状态参数 δ ( ) d p p q h c T T   = =  p T p c －定压比热容

Internal Energy & EnthalpyInternal Energydu=c,dTEnthalpyandh=c,dTdapplicable for all substances9

9 Internal Energy & Enthalpy v v u du cv dT ( ) T d   = + Internal Energy p p h dh c p dT ( ) T d   = + Enthalpy applicable for all substances

Property of Ideal-Gasideal-gas:no·Internal Energymolecularforcef(v,T)u=p25du = c,dT·Entralpy内能和烩都是温度的单值函数h=u+pv=u+RTdh =c.dT110

10 Property of Ideal-Gas •Internal Energy ( ) 0 ( , ) =   = T v u p25 u f v T v v u du cv dT ( ) T d   = + ideal-gas: no molecular force •Entralpy h = u + pv = u + RT p p h dh c p dT ( ) T d   = + 内能和焓都是温度 的单值函数