[PDF] 1erprincipe de la thermodynamique

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Pi āVi ā ȕ ā ȕā

ɵ Pf ā

Pi āVi āTi ā ȕ

ā ȕā ɵ Pf ā

Pi;Vi;TiPf;Vf;Tf

ȕā ȕ ā TiTf

=Cpm Cvm

āTf Pf/Pi

Ā āā V ā T

8><

TV1=cste

PV=cste

TP1=cste

ā PV=cste P/Vȕ

M() =() =;M() =;() =

;M() =M() =

0=P0= = 1;4 ȕā

ȕ ȕ V0=

C1C2 ć V0=;

ȕ P0=

āT0=

P0P0 T 0T0V 0V0I 0 R

ā CpCv

C1 ā ār=Ǭ ā C=

; I0=; āt=

ě ě ā C2 C1 ā

ā T1T2 ā

ā T2 C2T2=

ā ā T1C1

ā V1V2 P1P2

E ڔ

ȕě ā āT0 P0

ȕā T0

E m0= s=

ā V0= ȕ ā

ȕě P0=

ȕ P0x

S V

0 ě ā ȕě ā0=

h= ā ȕ ā g= ; Pi

ā x0x0sV0 ȕt= 0

ā xȕā āā

ā ā Pisxh

ȕ ȕ ā ā sxV0

ȕ2

āāfȕě

f ā mP= ȕ h= mA= ā ȕ T

āTȕg=;

ā Cm= 3R

A āā

ā ȕ ěT

āH=Qp+Wa Wa

Qp= 0 AT

ā ā ě ā C0

ā ȕ ā ě T=T0

ā C āT ā

ȕāTe ȕ āC

c=;

C ȕā ā ě ā ā

āT0 ā ā ȕ āt ā ā

P=h(TT) h ā

ȕā T

āȕěP0=m1=

ȕ ā T1= ā

c1=; m2 ā T2= ā

āc2=;āā

lf=

ā ěx=m2/m1 āx00x0 ě ȕā

ā ȕā ě x6x0 x>x00 x2[x0;x00]

T0=; ā ā

ām02m002 ȕ

m2= ā ě ȕā

ā ȕ m=; ȕ P=

P=; ě ā ā ā

P ā ȕ ȕ

Vf=;

ȕćVf

ā Patm ȕ ȕ

vf lv() =; (P ;h)

ā v=; ā ā

ā ȕ āT

ȕā A vi=; ā

M= m=

AB B

vf=;

ā ȕā ȕāA ȕāB

ā AB ě

ϔό (P ;h) āā

Q=W

PVā(PV) =PV+VP= 0ȕā

āāȕW=PV=VP=

PiViP

P PiPf W=Q=PiViPf

Pi

āŌPe=Pf W=Q=PfViVf=PfPiVi

W= U=RTf

TiCv(T)T

ȕ āā ȕ W=Pf(ViVf)

W=Pf nRTi

PinRTf

Pf = U=nR 1

TfTi!(1)

TiPf PiTf =TfTi Tf=Ti

1 + (1)Pf

Pi

W=PiVi

Pf Pi1

ā āā W=PV

U=CvT=Q+W!CvT=PV=nRT

VV1 1 T T=V V:

ā ā ȕ āā ȕā (TV1) = 0

ā Tf=Ti

Pf Pi

11 ȕā U=

PiVi1 Pf Pi 111
=W P P=V V @P @V S=P

V @P

@V T=nRT V2=P

V ā ȕ

ć =Cpm/Cvm>1

Cvm= 5R/2 ā ā

c=Cvm/MMȕāȕ

M= =c=; ě ā

ȕ c()=;

C= 3R!c=3R

M!c=;c=;:

āPV ā ā

ȕ 20 ţ ȕ 201;4'66

Pf= ā ā TV1=cste Tf=

T0(V0/V)1'3;3T0' ȕā āU=

P0V0T0(1)(TfT0)'; ȕH=P0V0T0(1)(TfT0)';

ȕ/(1)āȕ

Cv;m= 3R/2Cp;m= 5R/2 '1;67

ěSā ā

āāW=rI20tȕāě

ā ā U=

U1+ U2+ Uā ȕā ȕ ȕ

ā ȕ ȕ Ui=niCv;mTfTi=

PiVi1

Tf/Ti1 Cv;m= 3R/2 =cste

ā ā CT1

US=P0V0

T0(1)(T1+ T2) +CT1=rI20t

P0V0

T0(1)(T1+ T2) +CT1=rI20t:

T1= T0(1)

P0V0rI20tT2

1 +T0(1)

P0V0C!T1=:

ȕā ā P1P2 ā V1T2=V2T1= (2V0

V1)T1 V1=2V0T1T2+T1'; V2=2V0T2T1+T2'; P1=

P0V0T1/(T0V1) =P0T1+T22T0=P2';

ā P0V0/(T0(1)) =nR/(1) =; ā

ā ā ěSāā

S V0 ȕ

S ā ā ě

W=P0V0

ȕā ā U=W=P0V0=

nCv;mT T=nRT0/(nR/(1)) T=T0(1) ā

ā ā ȕ = 1;4T=

0;4T0 0= 0=

P0+m0g/S=Pi=;'P0

P(V0+s(h+x))=Pi(V0+sh)

P(1 +s(h+x)

V0)=Pi(1 +sh

V0) V

0 āx

P=Pi

1+sh/V0

1+s(h+x)/V0

ā x āhs

V0P=Pi

1xs V0

P0sm0g+PisPissx

V0 Fx=Pis2x

V0

ȕā x+!20x= 0!20=Pis2

m0V0

āf=1

2 qPis2 m0V0=;

ě V0= ȕ

s=Pi= m ȕ h=m=sh= f= ȕ

ě P ȕ A ā

Ei=mPgh+UP(T0) +UA(T0) ȕā

ȕā P ā Ef=UP(T0) +UA(T0+ T)

UA=mAcAT=mPghT=

H=Qp+Wa ȕ

H=cm1(TfT1) +m2(TfT2)= 0c ā

ȕ Tf=m1T1+m2T2m1+m2'32;8

ā ā C ě

ȕ ȕā cm1(TfT1) +m2(TfT2)+C(TfT1) = 0

C=cm2 T2Tf

TfT1m1c C/c'; ě

ā ā U2

R ȕ ā t

ȕā H=CT=U2

Rt T=T0+U2t

RC hćěȕ CT=U2

Rt+h(TT)t!T

t+T =T1 =C hT1=T+U2

Rh T=T0+ (T1T0)et/

ȕāāx00 ȕ

ā H= 0

x1 ě m=m1+m2ȕ

āT T > T0 ȕ x=x0 T=T0

m02 T2 Te ȕā

T2Te ȕ ȕ

H2=m02c2(TeT2) +m02lf

ȕ m1 T1 Te ȕ

H1=m1c1(TeT1)

0 = H= H1+ H2!x0=m02

m1=c1(T1T0) c2(T0T2) +lf=;:

ā ě m02

ā ā ȕT0 T0Q2=

m2c2(T0T2) +lf ā ȕ ȕT0

Q1=m1c1(T1T0)

x>x0 ě ȕ ā T0 x < x00 ȕ ā ā m002

Q1āā m1T1T0

T0Q1=m1c1(T1T0) +lf ā ā ā

m2 T2T0Q2=m2c2(T0T2) x00=lf+c1(T1T0) c2(T0T2)= 14;9: x6x0 ȕ ȕ T > x>x00 T < x2[x0;x00] ā

ā m02=; m002=; 2150

m02= x= 0;3 ɵ ā

ā m2T2Te ȕ m2

m1T1Te

0 = H= H2+ H1=m2c2(TeT2) +m2lf+m1c1(TeT1):

g= 0;63 ; P=Patm ȕā P=Patm

ȕ ā H=mlv ȕā U=

H(PatmV) =mlvPatm(VfVi)'mlvPatmVfVf'Vi

Qp ā ȕ W

W= UQ=Patm(VfVi) ȕ RPdV

Vi=Vf=; H=Qp=;U=;

W=; S=Sr=;

P ȕ ȕ

ȕāUHS ć

W= 0 ȕ ȕ

U=Qv=; ȕ Sr=Qv/T=;

āāSc= SSr=; ȕ ā

H=Qp ā

ȕā āTţ

ā ā T ;Ps(T)

T ;Ps(T) ā āā

ě H

ā ā ȕ ȕ Patm ȕ ā ě

ȕ Vf ć ā ȕ ȕ

U=Qv

āā v=; ā v

āh(T) =hv(T)h`(T)

ā Mā ȕā āT ȕh L

V ā āā ć hā āā ȕ

ȕ ě ā m=mv+m`

x=mv/m H ȕā ȕ ě ā ȕāH=mvhv+m`h`=mh`+mv(hvh`) ȕɵ h=H/m h=H/m=h`+x(hvh`))x=hh` hvh`=LM LV: ȕā A ȕā ě vi>v`(Ti) =; ȕā

B ā ȕā v=;/ ȕ

ȕā B āě x=hh hh=;:

ě m āā ā ā

Ā ȕā W=mRPv

v W1=m MRT0v vi=15 102;;

P ā

W2=mP(vfv) =(;;) =;:

W=;

ȕě ā m ā ȕ

Q= UW

H=U+PV)Q=mhm(Pv)W:

Q=()(;;;);=;:

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