工程熱力學(xué)

EngineeringThermodynamicsSAMChapterThree

PropertiesofIdealGasand

itsThermodynamicProcess

理想氣體的性質(zhì)及其熱力過程4/19/2025SAMThermalEnergyEngineeringDepartment3-1Summary

§3-1理想氣體的性質(zhì)

PropertiesofIdealGas§3-2理想氣體的熱力過程

ThermodynamicProcessofIdealGas4/19/2025SAMThermalEnergyEngineeringDepartment3-1§3-1理想氣體的性質(zhì)

PropertiesofIdealGas

1.理想氣體狀態(tài)方程Theideal-gasequationofstateFor1kgFor1kmolFormkgForn

kmol4/19/2025SAMThermalEnergyEngineeringDepartment3-2

熱力學(xué)能U為系統(tǒng)內(nèi)部各種形式能量的總和，包括內(nèi)部動(dòng)能及內(nèi)部位能。

系統(tǒng)的熱力學(xué)能可表示為系統(tǒng)溫度與比容的函數(shù)。狀態(tài)參數(shù)

理想氣體的熱力學(xué)能僅是溫度的單值函數(shù)，與比容無關(guān)。2.理想氣體的比熱力學(xué)能、比焓

Specificthermodynamicenergyandspecificenthalpyofideal-gas

比焓specificenthalpy：比熱力學(xué)能specificthermodynamicenergy：理想氣體

理想氣體的焓僅是溫度的單值函數(shù)，與壓力無關(guān)。通常規(guī)定：時(shí)理想氣體則4/19/2025SAMThermalEnergyEngineeringDepartment3-3Definition：比熱容

specificheat:可逆過程中，1kg物質(zhì)溫度升高或降低1K時(shí)所吸收或放出的熱量，稱為該物質(zhì)的比熱。3.理想氣體的比熱Specificheatsofidealgas比熱容摩爾熱容容積熱容僅對(duì)理想氣體適用比熱的主要的影響因素：①物質(zhì)的種類。②加熱過程。③物質(zhì)所處的狀態(tài)。4/19/2025SAMThermalEnergyEngineeringDepartment3-33.理想氣體的比熱SpecificheatsofidealgasDefinition：AsdescribedinfirstlawThatis比定容熱容SpecificconstantvolumeheatSpecificconstantvolumeheat04/19/2025SAMThermalEnergyEngineeringDepartment3-4比定壓熱容specificconstantpressureheat：AsdescribedinfirstlawThatisDefinition：Specificconstantpressureheat04/19/2025即理想氣體的、與v、p無關(guān)，僅是T的單值函數(shù)。SAMThermalEnergyEngineeringDepartment3-5對(duì)理想氣體理想氣體的比熱Specificheatsofidealgas

4/19/2025SAMThermalEnergyEngineeringDepartment3-6理想氣體的定容比熱與定壓比熱的關(guān)系

TherelationbetweenspecificconstantvolumeheatandspecificconstantpressureheatAccordingtotheexpressionofidealspecificconstantpressureheat,forsoThatis與理想氣體種類有關(guān)。對(duì)摩爾熱容與理想氣體種類無關(guān)。4/19/2025理想氣體的、、R、k之間的關(guān)系：SAMThermalEnergyEngineeringDepartment3-7

比熱比4/19/2025SAMThermalEnergyEngineeringDepartment3-8

真實(shí)比熱realspecificheatSpecificheatnotrelatetothepressurebutalsorelatetotemperature.ItisusuallyexpressedasthefunctionoftemperatureaccordingtotheexperimentTheheatcanbecalculatedbyrealspecificheat：Therealspecificheatappliestolargetemperaturedifferenceandhighprecision.4/19/2025SAMThermalEnergyEngineeringDepartment3-9

平均比熱

averagespecificheatSoDefinition：Theexperimentresultsofthespecificheatat25℃。定值比熱constantspecificheat4/19/2025SAMThermalEnergyEngineeringDepartment3-9

課堂練習(xí)：1.已知在1000℃時(shí)氧氣的平均定容比熱容為0.775kJ/(kg.K)，試確定其平均定容摩爾熱容、平均定容容積熱容、平均定壓比熱容、平均定壓摩爾熱容、平均定壓容積熱容。（參p56，例3-2）2.確定氧氣在730℃時(shí)的平均定容比熱容、平均定容摩爾熱容、平均定容容積熱容、平均定壓比熱容、平均定壓摩爾熱容、平均定壓容積熱容。4/19/2025SAMThermalEnergyEngineeringDepartment3-24.理想氣體的比熱力學(xué)能、比焓

4/19/2025SAMThermalEnergyEngineeringDepartment3-2討論計(jì)算的Δu

、Δh

的方法：①由熱力性質(zhì)表直接查取③利用熱力學(xué)第一定律的普遍關(guān)系，借助其它已知能量求取。a.按變比熱計(jì)算（經(jīng)驗(yàn)公式、真實(shí)比熱）b.按平均比熱計(jì)算c.按定值比熱計(jì)算②4/19/2025SAMThermalEnergyEngineeringDepartment3-11

5.

理想氣體的熵變

entropychangeofidealgas則可逆過程則soforinfinitesimalprocess：在閉口可逆過程中理想氣體4/19/2025SAMThermalEnergyEngineeringDepartment3-12

同樣可逆過程則理想氣體4/19/2025SAMThermalEnergyEngineeringDepartment3-12

可逆過程理想氣體4/19/2025SAMThermalEnergyEngineeringDepartment3-12

Theentropychangeofthefiniteprocesscanbetheintegralofthementionedexpression,fortheconstantspecificheat:（p,v）（T,p）（T,v）理想氣體理想氣體,比熱為常數(shù)理想氣體的熵變僅與氣體種類及狀態(tài)變化有關(guān)，而與變化過程無關(guān)，也就證明了理想氣體的熵是一個(gè)狀態(tài)參數(shù)。4/19/2025SAMThermalEnergyEngineeringDepartment3-13

標(biāo)準(zhǔn)狀態(tài)熵（絕對(duì)熵）standardstateentropy:Entropychangingoftheprocesscanbecalculatedbystandardstateentropyintheconditionoflargetemperaturechangingorrestrictcalculationrequirement.Definition:so：（T,p）T1T24/19/2025SAMThermalEnergyEngineeringDepartment3-14討論：求熱量的方法1、利用熱力學(xué)第一定律及其它已知能量求4/19/2025SAMThermalEnergyEngineeringDepartment3-2例3-3

（p59）氧氣被加熱后溫度從1000K升高到1400K，試計(jì)算每公斤氧氣的焓變化及熱力學(xué)能變化。⑴用常值比熱；⑵用平均比熱；⑶用熱力性質(zhì)表。4/19/2025SAMThermalEnergyEngineeringDepartment3-2例3-4

（p60）環(huán)境空氣狀態(tài)為T1=290K,p1

＝0.1MPa，現(xiàn)將0.2m3環(huán)境空氣壓縮到p2=0.5MPa,T2=600K,試計(jì)算該壓縮過程中空氣熵的變化。⑴按定值比熱計(jì)算；⑵按空氣熱力性質(zhì)表計(jì)算。4/19/2025SAMThermalEnergyEngineeringDepartment3-2例3-2

(華)

在空氣加熱器中，空氣的溫度從27℃升高到327℃，而壓力保持不變。試求加熱1kg空氣所需的熱量。

(1)按定值比熱容計(jì)算；

(2)按比熱容隨溫度變化的經(jīng)驗(yàn)公式計(jì)算；

(3)按平均比熱容表計(jì)算；

(4)按空氣熱力性質(zhì)表計(jì)算。可算得(1)按定值比熱容計(jì)算，加熱1kg空氣所需的熱量為301.2kJ/kg;(2)按經(jīng)驗(yàn)公式計(jì)算，加熱1kg空氣所需的熱量為309kJ/kg；(3)按平均比熱容表計(jì)算，加熱1kg空氣所需的熱量為306.81kJ/kg；(4)按空氣熱力性質(zhì)表計(jì)算，加熱1kg空氣所需的熱量為306.83kJ/kg。4/19/2025SAMThermalEnergyEngineeringDepartment3-146.理想氣體混合物mixtureofidealgases利用理想氣體混合物中各組元的性質(zhì)及成分來確定理想氣體混合物的熱力性質(zhì)，求出M、ρ、R、U、H、S、c……質(zhì)量守恒對(duì)存在化學(xué)平衡的混合物，有吉布斯等溫等容混合定律GibbsRule理想氣體混合物中各組元的狀態(tài),可以用該組元在混合氣體的溫度及容積下單獨(dú)存在時(shí)所處的狀態(tài)來表示,這稱為吉布斯等溫定容混合定律，簡稱吉布斯定律。該定律確定了在平衡狀態(tài)下混合氣體中各種組成氣體各自所處的實(shí)際狀態(tài)。（T,V,？）4/19/2025SAMThermalEnergyEngineeringDepartment3-14分壓力與分容積partialpressureandpartialvolumeSummaryofpartialpressure：道爾頓定律DaltonRule:pressureofidealgasesmixtureshouldbethesummaryofpartialpressureofthecomponents.partialpressure4/19/2025SAMThermalEnergyEngineeringDepartment3-15

partialvolume

Thesummaryofpartialvolumes：亞美格定律AmagatRule:

Thevolumeofidealgasesmixtureisthesummaryofthepartialvolumeofthecomponents.4/19/2025SAMThermalEnergyEngineeringDepartment3-15

分析：（1）分壓力pi是組成氣體i在混合物中的真實(shí)壓力，（２）對(duì)i組成氣體分容積Vi

不是i組成氣體在混合物中的真實(shí)容積。（真實(shí)容積應(yīng)為V）即組成氣體的分壓力與混合物壓力之比，等于組成氣體的分容積與混合物容積之比。4/19/2025SAMThermalEnergyEngineeringDepartment3-16

混合物成分components

ofmixturemassfraction：molefraction：Volumefraction：so

Relation：4/19/2025SAMThermalEnergyEngineeringDepartment3-17混合物的密度、摩爾質(zhì)量及折合氣體常數(shù)混合物的密度混合物的摩爾質(zhì)量4/19/2025SAMThermalEnergyEngineeringDepartment3-17混合物的折合氣體常數(shù)4/19/2025SAMThermalEnergyEngineeringDepartment3-17理想氣體混合物的熱力學(xué)能及焓混合物的熱力學(xué)能、總焓等于組成氣體熱力學(xué)能、焓之和。混合物的u、h按組成氣體參數(shù)的質(zhì)量分?jǐn)?shù)加權(quán)平均混合物的按組成氣體參數(shù)的摩爾分?jǐn)?shù)加權(quán)平均4/19/2025SAMThermalEnergyEngineeringDepartment3-17理想氣體混合物的熱容同理∵∴4/19/2025SAMThermalEnergyEngineeringDepartment3-17理想氣體混合物的熵

混合物的熵等于組成氣體的熵之和，即得注意：理想氣體的熵不僅是溫度的函數(shù)，還與p(或v)有關(guān)，因此上式中各組成氣體的熵值是混合氣體溫度T及各自分壓力pi狀態(tài)下的熵值。4/19/2025SAMThermalEnergyEngineeringDepartment3-17結(jié)論：4/19/2025兩剛性絕熱容器A、B，分別裝有理想氣體，氣體的定容比熱容分別為、，質(zhì)量分別為、，混合前溫度分別為、。求混合后的溫度T及。SAMThermalEnergyEngineeringDepartment3-17例：4/19/2025SAMThermalEnergyEngineeringDepartment3-18§3.2理想氣體的熱力過程

ThermodynamicProcessofIdealGasHypothesisconditions:

idealgas,quasi-steadyprocess理想氣體典型熱力過程

typicalthermalprocessesofidealgas:

定容過程isochoricprocess

定壓過程isobaricprocess

定溫過程isothermalprocess

絕熱過程adiabaticprocess

多變過程polytropicprocessKeypoints:4/19/2025SAMThermalEnergyEngineeringDepartment3-18§3.2理想氣體的熱力過程

ThermodynamicProcessofIdealGas分析熱力過程的主要目的thegoalofthermalprocessanalysis

:已知初始狀態(tài)過程性質(zhì)（1）確定系統(tǒng)的狀態(tài)參數(shù)：初、終態(tài)參數(shù)(p,v,T,s)間關(guān)系及過程方程式（2）確定過程中能量轉(zhuǎn)換關(guān)系:

（3）在T-s、p-v圖上對(duì)該過程進(jìn)行定性分析

主要依據(jù)mainfoundation

：Firstlawofthermodynamics;Stateequationsofidealgas;Expressionsofspecificenthalpy,specificentropy,andheatcapacityofidealgas.4/19/2025SAMThermalEnergyEngineeringDepartment3-18具體的假設(shè)與依據(jù)

：（1）假設(shè)過程為可逆過程（2）假定工質(zhì)都是理想氣體（3）假定比熱為定值§3.2理想氣體的熱力過程

ThermodynamicProcessofIdealGas4/19/2025SAMThermalEnergyEngineeringDepartment3-201.定容過程IsochoricProcessEquations:v=constantP∝T00[a?s?'k?r?k]

4/19/2025SAMThermalEnergyEngineeringDepartment3-20能量轉(zhuǎn)換情況04/19/2025SAMThermalEnergyEngineeringDepartment3-212.定壓過程

IsobaricProcessEquations:p=constantv∝T00[a?s?'b?r?k]4/19/2025SAMThermalEnergyEngineeringDepartment3-21定容線與定壓線在T-s圖上均為指數(shù)函數(shù)曲線;從同一初態(tài)出發(fā)的定壓線較定容線更平緩些。能量轉(zhuǎn)換情況04/19/2025SAMThermalEnergyEngineeringDepartment3-223.定溫過程IsothermalProcessEquations:

P-vdiagramandT-sdiagram:T=constantPv=constant0[a?s?'θ?:m?l]4/19/2025SAMThermalEnergyEngineeringDepartment3-22即定溫過程系統(tǒng)吸收的熱量全部用于系統(tǒng)對(duì)外作功。即定溫過程中系統(tǒng)軸功等于容積變化功。能量轉(zhuǎn)換情況4/19/2025SAMThermalEnergyEngineeringDepartment3-234.絕熱過程AdiabaticProcessδq=0絕熱可逆絕熱定熵可逆絕熱=可逆定熵絕熱過程：系統(tǒng)與外界不發(fā)生熱量交換時(shí)所經(jīng)歷的過程。一、定熵過程的分析[?d??'b?t?k]

4/19/2025SAMThermalEnergyEngineeringDepartment3-23Pv

k=cTv

k-1=c按定比熱分析按變比熱分析分析方法

1.按定比熱分析定熵過程積分可得理想氣體過程方程式Equationsisoentropicprocess[a?s?n'tro?p?k]

isentropicprocess4/19/2025SAMThermalEnergyEngineeringDepartment3-23Pv

k=cTv

k-1=c參數(shù)關(guān)系：4/19/2025SAMThermalEnergyEngineeringDepartment3-23從同一初態(tài)出發(fā)的定熵線較定溫線更陡些。q=0能量轉(zhuǎn)換情況:4/19/2025SAMThermalEnergyEngineeringDepartment3-232.按變比熱分析定熵過程

這種方法存在的問題：①依然是一種近似計(jì)算。②當(dāng)終態(tài)溫度不知道時(shí)，需要試算。方法：先假定T2，計(jì)算出κm，按過程方程式計(jì)算得出T2，修正T2重復(fù)上述計(jì)算，直至假定溫度值與計(jì)算溫度值相同（接近）時(shí)，所得的κm即為所求。

當(dāng)溫度變化幅度較大時(shí)，按定值比熱容方法計(jì)算所得結(jié)果誤差較大，因而需采用變比熱容進(jìn)行計(jì)算。

（1）平均絕熱指數(shù)法過程方程表示為＝常量平均絕熱指數(shù)法圖表法A:利用熱力性質(zhì)表中的標(biāo)準(zhǔn)狀態(tài)熵B:利用空氣熱力性質(zhì)表中的相對(duì)壓力與相對(duì)比容4/19/2025SAMThermalEnergyEngineeringDepartment3-23（2）圖表法

上式可改寫為由有T2T1A:利用熱力性質(zhì)表中的標(biāo)準(zhǔn)狀態(tài)熵4/19/2025SAMThermalEnergyEngineeringDepartment3-26例：（p69例3-5）例：（p69例3-6）則pr～T定義:則則vr～T定義:則T2T1T2T1B:利用空氣熱力性質(zhì)表中的相對(duì)壓力與相對(duì)比容變比熱容絕熱過程中系統(tǒng)能量轉(zhuǎn)換關(guān)系可直接按能量方程式求取：

4/19/2025SAMThermalEnergyEngineeringDepartment3-245.多變過程PolytropicProcess多變指數(shù)polytropicexponent

n∈（-∞，+∞）Equations:四種典型過程均為多變過程的某種特例：當(dāng)n＝0時(shí)，pv0＝p＝常量，即為定壓過程；當(dāng)n＝1時(shí)，pv＝常量，即為定溫過程；當(dāng)n＝k時(shí)，pvk＝常量，即為絕熱過程；當(dāng)n＝±∞時(shí)，p1/nv＝p0v＝v＝常量，即為定容過程。[p?l?'tr?p?k]

4/19/2025SAMThermalEnergyEngineeringDepartment3-245.多變過程PolytropicProcessRelations：（）Equations:4/19/2025SAMThermalEnergyEngineeringDepartment3-25（）Energy：（）多變比熱4/19/2025SAMThermalEnergyEngineeringDepartment3-26Analysisonp-vdiagramandT-sdiagram：(1)從定容線開始，過程的多變指數(shù)按順時(shí)針方向遞增；(2)過程中能量轉(zhuǎn)換情況也可在圖上定性分析4/19/2025SAMThermalEnergyEngineeringDepartment3-26(2)過程中能量轉(zhuǎn)換情況也可在圖上定性分析4/19/2025SAMThermalEnergyEngineeringDepartment3-264/19/2025SAMThermalEnergyEngineeringDepartment3-26Discuss：Howtosolvethepolytropicexponentn?4/19/2025SAMThermalEnergyEngineeringDepartment3-26（參p74例3-7）4/19/2025SAMThermalEnergyEngineeringDepartment3-26（參p75例3-9）4/19/2025SAMThermalEnergyEngineeringDepartment3-26例：（參p74例3-10）要記住結(jié)論：盛有理想氣體的剛性容器絕熱放氣過程中，剩余氣體經(jīng)歷一個(gè)定比熵過程。4/19/2025SAMThermalEnergyEngineeringDepartment3-26（參p79習(xí)題3-6）4/19/2025SAMThermalEnergyEngineeringDepartment3-26例：剛性絕熱容器被隔板分成相等的空間，隔板一側(cè)裝有1kg空氣，p1=0.1MPa、T1=300K，另一側(cè)為真空，當(dāng)抽去隔板后，空氣充滿整個(gè)容器、達(dá)到新的平衡。求過程中空氣的△u、△T、△s

及終態(tài)壓力p2

。4/19/2025SAMThermalEnergyEngineeringDepartment3-26思考題(17)：試說明下列常見過程的基本特征：⒈絕熱節(jié)流過程；⒉由穩(wěn)定氣源向剛性真空容器的絕熱充氣過程；