Hristev - Raspunsuri

7/18/2019 Hristev - Raspunsuri

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in a lti-e aer

a.

16 kg/m 3 .

!Y.U= Q .

= 12,3 L .

Pl - 1) =

700 J .

=8 ,72 kJ .

2.2.1 4. a) h2=h(T2IT1 =40em . b) L=pt,v=(H+mgIS)S(h 2-hl)=

= (H S + mg) tilt. T I T1 =109,8 J . e) Q =vCp t. T= v (7R 12)(T2 - T l) =

= (7/2)(PV2 - pV 1) = (7/2) L =384 ,3 J . d) t.U =vCv(T2 - T 1) =

= v (SR 12)(T 2 - T1) = (5/2) L =274 ,5 J .(4) .2.2.15. a) Q = vCp!Y.T = (ml Ji )[(i +2)/2 ] R !Y.T, m = 2 .;l-Q) : [(i + 2)R !Y.7] =

= 11 ,0 g. b) L = vR(T 2 - T1) = [21(i +2)] vCp(T2 - T 1) = [21(i +2) ] Q =207 ,9 J .e) !Y.U= [i1(i +2)] Q =623,6 J , Q = !Y.U+ L. d) !Y .E= (i / 2) k!Y.T =

=4,14 .10- 21 J .2.2.16 . a) Q = [(i+ 2)/2] pV 1 (V21V1 -1), V21V1 =1 + [21(i+ 2) ] .

. QI(PV1) =2 ,0. b) L =2Q l(i +2) = 202 ,6 J . e) !Y.U= i QI(i +2) =506,6 J .

2.2. 17. t.U= Q- L = Q- (H + mg l S)( ~- V) =Q - (H + mgl S)V '. (TilT - 1) =Q-(H+ mgIS)V t.TIT={33 JJ

2.2:18 . Q = [(m1 1#1 )Cp1 +(m2I Jl2)C ~J( f; - T1) , pV1 =(m1 1#1 +

+ (m 2/#2) RT1 ' Q = pV1(T21T1 -1 ) {1+(C v1 #21 ,l1+ C v2 m21m1) :

: [RCJ l21 #1 +m 2 I m 1)] } = 300 J .2.2 .19. a) t.Ep = mog t.h , t.V= S t.h ~ t.V= S t.Ep/(mog) ,

V{=V2 - t.V =(m Ip.) RT 2 : (H + mog I S) - S t.Ep : (mog) = 2,5 L.

b) T1 = [u I (mR)] (H +mo 9 IS) V1 = 300 K = 27°C .e) L = p(V2 - V1) = (m / Jl) R(T2 - T 1) =16 ,6 J sau

L = (H + mog / S) S t.Ep : (mog) = [HS I (m 09) + 1 ] t.Ep .

d) Q = vCp(T2 - T

1) = v (7 12)R (T 2 - T

1) = (7/2) L =58 ,2 J .

e) t.U = vCv(T2 - T 1)= v (5 12)R (T2 - T1) = (5/2) L = 41, 6 J .2.2.20. Q = met, + mvi1, mv =(Q - mc tf) : A = 2,62 g . h = m; RT f:

: (tlpS) = 44 ,5 em .2.2.21. H =H - F I S + pgy ~ F =pgy S ;

F

Fig.2.2.21 R

FHS ---- ----_--- .... ., ...H

Ty

_______ H yH (0 h=H/( pg) h '

L = (1/2)HS' h + HS' (h I - h) = H 2S I (2pg) + HS[h' - H I( pg)].L = HS[h' - H I (2 pg)] = 10 ,13 J . V.fig.

2.2.22 . L = P2(V 3 - V2) = vR(T3 - T2)= vRT 1 (1 - T2I T1) = vRT 1 (1 - 1 / k) =

=4 ,15 J , unde T2/T1 = P21P 1 =11 k , T1 = T3 ~ t.U= 0 (ga z idea t!) V.fig.2.2.23 . Q = v R T1(T2 I T1 -1) =v R T1(V2 I V1 -1) , V3 I V1 = V2 I V1 = 1 +

+ Q I( vRT 1) =3 ,0 sau (!y'U =0) Q = L =P1Vl(V2 I V1 - 1) =v R T1(V2 I V1 -1).V.fig.

301



P\

\

1 \\

\ izo t.\

\ ,". " - , 3

2

0

P \

\

21 \\

\

\ ,

izot> . ,"3 ~

v p

3

2 I 1 2 3I I /

/I

I/ /

V 0 71=73 T 0 71=7 3Fig.2.2.22 R

V P

2 1 2

o V 0 7;=T3 TO' 7;=T3Fig.2.2.23 R

2. 2 .24. Q' = [(Cp - R) 1 R ]mgh, Q " = vCp T (n - 1) + [Cp 1 R] mgh (n-

Q = Q' + Q" = mgh (n Cp 1 R - 1) + vCp T (n -1) =3 ,2 kJ .

2 .2 .2 5 . L = vR(T3 - T2 - T4+ T1), Tl = Ti = T1 T3,

L=vR(T3 - 2 ~T1T3 + T1) = vR( J G -fT; )2 =831 J . V.fig.

P V P\

\

2 3\

\

.izot.\ "\

""# "

4 3cz:4 /,/ Z OOI / 2, I

I /, '

"'

41

o V 0 7;=T4 T 0 7;=T4Fig.2.2.25 R

2 .2 .26. L = (a -1)(jJ -1) P1 V1 ' P1V1 =vRT1, P3V3 = af 3pl V1=vR(T1 + -L = (a - 1)(jJ - 1)vR~ T: (af3 - 1) =249 ,3 J . V.fig.

2. 2. 27. Q = vCp(T3 - T) + vCv(T - T3) = vRT(T31 T -1) ,V31V1 = V21V1 = T3IT= 1 + Q/(vRT) =2 ,0. V .fig.

\2.2 .28 . L = P3(V3 - V1) =vRT1(1 - P3IPl)' T1 = L : [(1 - 1/n )vR] =30V.fig. 2 .2.31 R.

302

2

P 1_ t

0 V1

P \

\

1 \ ,,\ ,

izoi : \T ""

0

2.2.29. L =2.2.30. Q == T1 + 4Q:

2.2.31. P1

T1 = (L

P

P1

2.2.32. T3

=350 K.2.2.33. La-

siunea atmos fedestinde izobar



3

7 1=7 3 T

..T

m g h (n -1) .

3.

T

vR(T1 + t,. 7) ,

~ =300 K .

o T

v p

2 3 4 3 2 3

17/7:, ,/2 l 'I ' " I I

I • • . ., I / ,;4,I . " I : I"" I I

I... I I' I I

~~- - - - - - - - - - ~~

1 "' - - _ - -. 4: V

o T4<T2 T 0Fig.2.2 .26 R

p v p,\

1-, .. .-+--. 3,\

\

\

2 ~ -+- .. .. " .3 1 ~-+-....".3

izot : ,T"" -,

2 '

o V 0 T,= T2 T 0 T1=T2 TFig.2.2.27 R

2.2.29. L = (P1 I n)(V2 - V1) = (m I fi) RT(1 - 1 In) = 830 k J .2.2.30. Q = vCv(T2 - T1) = v Cp(T2 - T3), T2 = T1 + (Q/v)(1/Cv - 1/Cp) == T1 +4Q : (15 vR) = 350 K .

2.2.3 1. P1V 1 = P3V3 = P2V3 =vRT 1, L = P3V 3(1 - V1 I V3) = vRT 1(1 -1 In) ,T1 = (L I (vR)] [1 : (1 - 1 In)] =300 K .

P V P

2""-~~3/

/

/

- \ 1'P1 \

\

3

" izot .,, , ,

1..&-.••••..•/

/

/ To V 0 71=73 0 71=73 T

Fig.2 .2.31 R2.2.32. T3 = T1+ QR I (v CvCp) = T1+ QR I (v 15R 21 4) = T1+ 4QI (15 vR) =

= 350 K . .2.2.33. La inceput , presiunea gazului va creste izocor pfma eqa leaz a p re-

siunea atrnos ferica : T': T =H: (H I n) =n, T' =nT, dupa c are gazul sedestinde izobar . Q =vCv T(n - 1) + v(Cv +R) T n(k - 1) =47,4 k J .

303



p IQ I v pV

\3,< 1

i73 22 V2,

,\ " ., T :J' ,~ " -, ~-- Q,0,. . . . . .. .T 1 .. .... ... : ~ 3

~ 1I~ 11

1 - ~ ~, ~ 1, ,1

o V 0 71<T3 T 0 71<T3Fig.2 .2.32 R

2.2.34. Q1 = vCp(T3 - T1) + vCv(T1 - T3) = v R(T3 - T1), Q2 = vCiT4 - T. -

+ vCp(T1 - TJ =v R(T1 - TJ ' Q1 - Q2 = v R(T3 - T1 - T1 +TJ == v R(T3 - 2T1+ T1 2I T3) = v R(T3 - T1 )21 T3 =831 J . V.fig.P V P

,l' 3 2 3.rzWZOJ

I ' 1" 1

I ",I "

"

4

, , ,\{zot. ,if,, ,"-' ... ..2

o o o T1=T2Fig.2.2 .34 R

2.2.35. Q = v(2Cp - Cv)( T4 - T1) = v(2R + CvMT = v(7R 1 2) Il = 2,91P \ V

1 2 \ \- ~ - - - , '1'!""'-+-' 2, ', ,~

~ , ',0-:"Or'" \, \, \,

. 3'f-+- ... .• . . .1"_ 4 ---1

1

1

V T

p

3 ~ -+ - ...,.. . .2,, I

'I 0: 0·" ' 1\ 'V

/ . .. . , I

" '

3"'-~ __,,,,

o T 0 ~=V3 V 0 T

~ ~ 0Fig.2 .2.35 R2 .2.36. L =- vRT1(T41 T1 -1 )(V21 V1 - 1) = -vR (T4 - T1)(V21 V1 -1 ) =

== - 831 J . V.fig.2.2.37. F = (p - po)S =can st ~ P =can s t. (1 /2)Mv2 = (p - Po)!':..V =

= (1 - 1 In ) vR!':..T, Q = (C v + R) Mv2 : [2R (1 - 1In)], Qo = (C v + R) Mv2 : (2

304

2 .2 . 3

2 . 2 . 3

= (mIJl )2.2.2 .2 . 4

= 2,3 kJ

=[1 I( y-

Fig.2.2.5



2

Cy(T 4 - T, ) +T, +T~ =

T

T = 2,91 kJ .

• .. , . ..r 2rrrrr

T-

t\v=

Mv2 : (2R) .

T

vp P4 ~ 33

'If

'I'1•..

11 2 1

;VT 0 V1 V2 0

\/ 1 rv1 - r

I' , , ,4,1 , ,( r r

I " I I I

74<72c)

Tb)

Fig .2.2.36 R2.2.38. a) L , vR Tfn(p,lp,) , P, V,ln(p ,Jp,) , 271.8 J . b) Q ' L. c) I1U , q.2.2.39 . a) p, , e P, ' 275 kPa , V,, (1Je)mRT: (!'P,) , 9,1 L b) Q ' L,

= (mi,l . ) RT/n(lIe) = - 2,3 kJ , c) t\U = O.

2.2.40. Q , (m f!') RTfn 2, u2 , 3RT! " ' 3Q: (m In2) , u' SOD m/s.

2.2 .41. tf2 , 3RT! II. P, V, ' (m I II RT, L, (mtf 213) In(mt f2 : (3p, V , J J '= 2,3 kJ , b) Q =L , G )su =0 .

*2.2.42. L = - t\U =- vCvt\ T, t\ T =- 2L : (i v R) = _ 10K.

2.2 .43. L = - !::J .U - vCyt\ T, T2 = T, - (21 i) ul: : (mR) =270C .

2.2.44 . 120t. p,lp, ' V,IV, ' n; ad. p,lp, ' (V,IV,) Y, nr > n (y> 1) .

2.2.45. T,I T, ' (V, I V,r' , F (i 2)1 i , i, 21g(V, I V,) : Ig(T,IT,) , 5.2.2.46 . 7f I 7i =(1IjI Vf ) Y-l =zH . Tl1 T2 =ZY1-1 : zYr1 = 1,2 .

2.2.47. a ) P ,' P,(V ,I V,) ' , 38 kPa . b) L, _ AU, _ (e,1 R)(vRT,-- VR74) =(Pl V, - P2 V2) / (y - 1) =- 405 J . c) ~U = _L .

2:2.48. L, (P, V, - P,V,) I( Y -1), - L' , P'V,/( P, V,), T,IT, ' 1 ++ (1 - y) L : (P l V,) = 5000C.

2.2.49. T2 = r , [1 + (y - 1) W /t»,V1)1 = 773 K =5000C .

2.2.50 . V.fig. Lad/ L;z ot=[- vCy(T2 - T,) l ; [vRT1

In (V21

V,) l =

' (1 I(y - l))f(V,I V,) '-'1 : (-In (V,I V,)1' (1 I(y -1) )(, H _ 1 ) : In , , 1 ,1 5

Fig.2.2.50 R

p

p

o

305



b)Fig.2.2.54 R

2.2 .5 5 . a) L =(1/2 ) a(Vl- V12) = 150 J . b) ",, "u = ( i 1 2 ) (p2V2 - P1 V1) =

7= (i /2) a(Vl- V1 2) = i L =750 J . c) Q = ",, "U + L =900 J . d) Q = ",,"U+ L =

= [(i+1)Ii]vCy"""T=nC,,,,"T, C= [(i+1)/i] Cy= [(i+1)/2]R=24 ,9J /(mol -K)_2. 2 .5 6. pI)< = const -- -+ TlJ -1 = cans t ~ "fp1-k =const sau Tp(1-k)lk =con st.

a) L = vR(T1 - T2) : (k":' 1) = (p1 V1 - P2 V2) : (k - 1) , b) °= """U + L=

= v [Cy + R/(1 - k)] (T2 - T1) = v C """T. c) C = C v+ R/(1 - k)= Cy(k - y) : (k - 1).2 .2.57. L =- """U =- vCy(T1 - T2) = vCy T1 (n I k - 1).2 .2 .58. L1-2 = -vCy(T2 - T1), 0 2-3 =vCy(T3 - T2) ,

L1_2 = 0 2 -3 -- -+ - (T2 - T1) = T3 - T2 -- -+ T3 = T1 . V.fig .P 1 V P

\ 1\ 1

\ 1

p

1

oa)

1

2

T 0

1

13 2

a d iV/ / 1 ',,,,,,

v 0c)

3

:i,, , "'

~ <..' a d.T a T

c)

2 - J0 1 --- - -- - . -aa)

306

1

b)Fig.2.2 .58 R

T

o

22 .

v

4I

I

I .-.-"

o

2 .cem izba te le tficul prpe pO f1Jgazu lsepe portiprirne s tepo rtiun eraces te ,cald uralucru mdedi t caenerg ia -deci a icipe po rtise lncalzdeaza ca



2.2.59. L= (112) (vRT2 - P1 V1 . T3/ T1 - P1 V1 . T2/ T3+ vRT1) == [mR / (2 !~ )] (T2 - T3 - T1 T2/ T3+ T1) =20 ,75 J . V.fig .

V P

y-1)/(2y)=

P

at omi ce

84, 3 J .

V1) =

0 k J .

a2

T

V1) =L=

mol·K).

=co ns t.

(k -1) .

b)Fig.2.2.59 R

2.2.60 . T2 = T1 + W RT 1 / (P 1 V1Cy) =T1 [1+ R W / rc ,P1 V1)] = 284 K .2.2.61. In diagrama P - Vs e vede imediat ca L123 > L134. V.fig.

P P\

2\

1lS J0-: ",

4 3 ' ,--

T 0 Vb)

Fig.2.2.61 R

a)

2

1

V

4

3

I,1/

'/a

a)

V a T'"I T c)

T

1 2

4I

I /

,/

/

'/a

c)

2.2.62. V.fig. Ou-cem iz otermele ~ adia-bat e le tangent e la g ra-ficul proces ului . Atuncipe p ortiunea CAMOga zul se incalzeste , iarpe portiunea AMOSprime s te ca ldura . Peportiun ea OS gazu l se

races te , des i prirne s tecaldura (fiindca fa celucru m ecanic mai m ultdecat ca ldura pr imita ~energia interna scad e),de ci aici C < 0; la felpe p ortiunea CA gazul 0se Incalz es te , desi ce- ,de aza c aldur a , deci ~ aici C < o.

P

Fi~2 .62 R

307



2.2."63. Q = (1/2) m rvr2 = (1I2)[mM I (m + M)] v2 =t:.U =vCyt:.T,

t:.T= [1 I (2vC y)] [mM I(m +M)] v2 = 0,72 K.

2.2.64. F = (p - Po)S =const ~ p =const , Q =v Cpt:.T; (p - p o>t:.V =

= (1I2)Mv 2, p(1 -1 In) = (1I2)Mv 2, vRt:.T= (1/2)Mv 2: (1-1 In), Q == vCpt:.T= (Cpl R) (1/2)Mv 2": (1-1 In) = [y I(y -1)](1I2)Mv 2: (1-1 In) =

= 1,4 kJ . n ~ 00: 0 0 = [yl(y -1)] (1/2)Mv 2= 0,70 kJ .2.2.65 . h = [Mgho + (m I Ii.) Cy1] : [Mg + (CvI R )Mg] =

='[ho +m CyT /('I.Mg)]: (1 + CvlR) = 55 cm .

2.2.66 . Q =vC(T 2 - T1) =(C I R) (vRT 2 - vRT 1) = (C I R) (P2V - P1 V) ,

P2 = P1 + QR I(CV) = 133,3 kPa .2.2.67. Q2 - Q1 = (1I2)(V 2 - Vo)(Po + P2) - (1I2)(V 1 - Vo)(Po + P1) =

= (1/2) P o(V2 - Vl) + (112) Vo(P1- P2) >0 , deci in procesul 2 (AB 2) .

2.2.68 . (P1 + Mg I )(Vl r) I T1 = (Pl' + Mg I S)(Vl'l r ') I T2, Vl + V2 =

= V1' + V2', [(r' -1) /(r-1)](T21 T 1) = (1 + 1/T) 1(1 + 1/r'),

r'2-r ' [(r2-1)/r] TlT 2-1 =0 sau r'2-2r'-1 =0, r' =1 ±J2= 2 ,41 .

2.2.69. 1) V. fig. 2) L este minim pe adiabata (c), 3) t:.U > 0 pe izobara,t:.U = 0 pe izoterma , t:.U <0 pe adiabata .p V P

izob . a aV2 - - --

c

(

,, I

, I

,','ad .

V1 - - - - '1' ad., ' ,, -,,,

o oa) c)

./

b). Fig.2.2.69 R

2.2.70. P2 1 Pl =V4 I V3 =P31P4' P3 =P4 . Vl V 2 =P1(Vl V 2)2 =25,0 atm.,p, V P

' 3,,\

\

\

P 2= P 1 .~2~0<"

1 4,....~-...,. 3

4

1 ' .'- -

o V 0 T 0a) b)

Fig.2.2 .70 Rc)

308

T

=

=

L=

o

T

L=v

p

o



2.2 .74.d 3= VIN,p=(NIV)kT ~ d 3=kTlp , ~kT/p =3 ,3nm.2.2.75. p = H <to I ef , F = (H - p) S = m an= mw2 e .

n2 = H(1 - e /I e l')s : (me ) = 31,36 rot2/s 2, n =5 ,6 rot/s.

2.2.76 . pV I (RT 1) + pV I (RT 2) = p' . 2V I (RT') . /).U = (Cyl R) . L'1(PV) .

(Cyl R) p" 2V - 2(C yl R) pV ~ p' = P ', T' = 2T1 T 2: (T1 + T2) = 102°C.

2.2 .77. v1 + m21 p = p' V I (RT') , v1CJ1 + (m21!l) CJ 2 = C v' p 'V I R ,

T2 = (P 'V IR-v1 T1): (m 2/lt) = 310 K .2.2.78 . m1 IIt1 + m2 /lt2 =P '(V1 + V2) I (RT ') , v1 CY1T1 + v2CV2 T2 =

=v1Cv1 T' + V2Cy2T '. v =pV I(R7) , T'= (CV1 P1V 1+ CV2 P2V 2): [R(CV1m 1 1111+

+ CV2m21!(2)] =306 K . p' = (m1 1111+ m21P 2) RT': (V1 + V2) =2 ,10 MPa .2.2.79. pV 1 = (m1 Ill)RT, pV2 =(m2Ifl)RT; (P + L'1p)(V 1+ L'1V)=

= (m11J1)RT 1, (P + L'1P) (V1- L'1V) = (m2 I II)RT 2 ' I1pVo = (m1 l,u)R(T1 - 7) +

+ (m2Ip)R(T2 - 7) . Q =L'1U1+ L'1U2= (m1 Ifl)Cy(T1 - 7) + (m21 11)C v(T2 - 7).

L'1pVo= QR I c ; ~ L'1p= (R I Cy)(Q I Vo) =(2/3) Q I Vo =6,67 kPa . .

2.2.80. T' = (v1 Cp T1 +1>\2Cy T2) : (v1Cp + v2Cv) = (v1yT1 + v2 T2) : (v1Y + v2) =

= 410 ,5 K . M = -[1 : (HS + Mg)] v1v2R(T1 - T 2) : (v1Y + v2) = - 8,0 em

2.2.81. V 1 : V2 : V3 : . .. : Vn = 1 : 2 : 3 : .. . : n ~ Vk =k V1 '

V= V1 + V2 + •••+ Vn = V1(1 + 2 + . .. + n) = (1/2)n(n + 1)V1 ' p V In =PkVk ~

P k =p(n + 1) I (2k) = P1 I k ,P 1 =p(n + 1) 12 . P« = Pk+1 + mkg IS .

P1Ik = pl(k + 1) + mkgl S ~ mk = (Splg)(n + 1) I [2k(k + 1)] .

2.2.82. p(f) =H [V I (V + v)]nt, In(H I p) = nt· In[(V + v) I v].

tg a = n In(1 + vl V), tg f3= n In(1 + v21 V), (1 + vl V)tg/3 = (1 + vi V)tga ,

V2 = V [(1 + VlV)tg/3/tga - 1] = 210 em 3 .

2.2.83. Oueem famil ia de adiabate ; douaV adiabate vor fi tangente la eielu, aeolo Q = O.

Pe portiunea CSO gazul prirneste caldura(dQ=TdS> a) , iar pe portiunea OAC cedeazaealdura (dQ = TdS <0) . Pe portiunea SO(respeetiv AC) caldura speci fics C =QI ( vL'17)

es te negati va , deoareee gazul , desi pr irnestecald wa (Q > 0) , se raceste , L'1T <0 , aeeastalnse arnna ea etectueaza mai mult lucru me-canic decat caldu ra p rimita , pe seama scade-

o rii ene rgiei interne (de aceea seade tempera-

Fig.2.2.83 R t ura) . V = [mR I (a p)] .T , dee i panta izo -barelo r este inve rs propor tiona la cu pres iun ea.2.2 .8 4. L = (P 2 - P 1)(V3 - V1) = [P1 T3V1 I (T1 V3) - P1 ](V3 - V1) =

= (P 1 V1 I T1)(T31 V3 - Tl V1)(V3 - V1) == (PoV 1oITo)( T31V3- TlV1)(V3- V1) = 24,7 J ,

und e am a dus produ sul P1 VlT1 la co nditi! nor male de presiune ~ tempe ratura .

o



3,3 nm .

. t :.(PV) .

= 102°C.p'VIR,

CY2 T2 =y1m1/,u1+

0 MPa .

=T1 - 7) +

v C T2 - 7) .a.

1Y + v2) =m

eoete; douacol o Q =O.calduraAC cedea zaune a SOC =Q/(vt:. 7)

~ prirneste0, aceas tat lucru me-am a scade -e t empe ra-pant a izo-

) --

em peratura.

v P2

P3

3 P 2 2 3JJJ

JJ

V1J

I ,, 1 4 1J J P 1 I

I J" JI ,

,", (J J

VI,

, J ~T J I '

0 T1 T3 0 V1 V3 0 T1 T

a) b) c)- Fig.2.2.S4 R

2.2.85. pV= vRT= vR ( aV - bV2) ~ P

p =vR (a - bV) , v.fig. L= (1/2) (P 1 + P2) . 1. (V2 -V1) = (1/2) vR(2a - bV 1 - bV2)( V2 - V1) .

t:.U =vCyt:. T = [vR I (y - 1)J[a (V2 - V1) -

-b(Vl- v12)], c; = R I (y - 1) ,Cp=yRI(y-1) , Cp-Cy=R , y=Cp/C y.

JQ = su - Ll [vR I(y -1)](V2 - V1) .

. [a - b(V1 + V2)T- vR (V2 - V1) . 0 V1 V2 V. [a -b(V1 + V2)/2]. Fig.2.2.S 5 R

"2.2 .86 . a ) '7 = (T1 - T2) : T1 = 40 %. b) Q1 = L 11] = 1,00 kJ .c) IQ21 =Q1 - L =0,60 k J .

2.2 .87. IQ21 = f Q1 ~ fQ1 I Q1 = T2 I T1 ~ T2 = f T1 =300 K = 27°C,'7 = 1 - I~ 21 I Q1 = 1 - f = 40 % .

V

b)CICLUL CARNOT

Fig.2.2.S7 R2.2.88. Ljzot = Q1' Wi z o t= IQ21 ' '1 =1 -IQ2 1 I Q1 = 1- W iz o tI Lizot 'VV;zot=(1 -17) Lizot=SOJ . V.fig .2.2.S7 R .

P,I

\ , 31

o o Ta)

P1

oc)

T

•••

311



pv

pI

\ I

\ I

'I

I

I

1

3 ' 1 i~~~1 3,'> ad.

V 0 T 0 Ta ) b) c)

Fig.2.2.103 R

V P3 1

2

31

, , ' 3,

V 0 T 0 T

o

p

oa ) b) c)

Fig.2.2.104 R2.2 .105. a) 01 =v(7R /2)(T2 - T1) + vRT21n(Pl p,J = 10, 0 kJ .. b) 1 021 =

= v(7R /2)(T2 - T1) + vRT11n(P1 / p,J = 8,3 k J . c) L = 01 -1021 = vR(T2 - T I

. In(P1 / e» = 1,70 J . d) 7J =L / 01 = 17 %. e) 7 J e= 1 - T1 / T2 =40 % .f) 7J= [vR(T2 - T1)ln(P l p,J] : [vCp(T2 - T1) + vRT21n(Pl p,J] =

= (T2 - T1) :{ [y / (y - 1)](T2 - T1)/ In e + T2 }< 7J e = (T2 - T1) / T2 .

P V P

3 1 •.. 2

,

"3

4 3", ,'1/, ,

0 V 0 T 0 Ta) b) c)

Fig.2.2.105 R2 .2.106. V.fig.2.2.1 05 R . 17 = (T2 - T1) : {T2 + y(T2 - T1) : [(y - 1) Ins ]} <

< 1 7e = (T2 - T,) : T2·

314

I ] = [( p - 1)

2 .2 .10

. In(V4/ V1)

7Je = 1

T2\P ' 2

I ,r;\

,,

o

2.2 .1 08 .

b) 01 = vCv(

17= I(y - 1 )1 7 e = 1 -

2

I1

o

< 'Ie =

17 = 1 - T32.2. 111 .1/

+ pe ( Y - 1) In f.

(F .= T3/ T1, P



T

T

2

3

--

<

'7= [( p - 1) In e ] : [y (p - 1) I ( - 1) + pin e ] =2 2 %, "c = 1 - 11r = 50 %.2 .2.10 7. Q1 =vCv(T2 - T1) + vRT21n(V41 V1) , IQ21 =vCv(T2 - T1) + vRT1

. In (V4IV1) , n = [( r-1) In c :]: [(r-1)/(y-1) +z In £] = 28 % ;

17c = 1 - 1 IT =50 % . V.fig.

T2\ Vp \ 2\

\

b)Fig.2.2.107 R

2 .2 .1 08 . a) L = vR(T3 - T2 - T4 + T1) = vR (T2 - T1) (T3 - T2) I T2=627 J .b) Q1 = vCv(T2 - T1) + vCp(T3 - T2), IQ21 =vCv(T3 - T,J + vCp(T4 - T1),

n= [ (y - 1) (s - 1) (0 - 1)] : 10 - 1 + yO (s - 1)] = 13 % ;'lc =1 - T1 1! 3 =1 - 1 I (c:o) =83 % . V.fig.

V

b)Fig.2.2.108 R

2.2.10 9 ." = 1 - T31T2 < 'k: =1 - T41T2, (T4 < T3);

,,= 1 - T31T2= 1- 1 ley-1 = 51 %. V.fig.

2.2.110.1/=1-IQ21/Q1= 1-(T3-T,J/(T2 -T1)=

=1 - [T3(1 - T41 T3)] : [T2(1 - T1 I T2)] = 1 - T31 T2 << "c= 1 - T41T2, (T4 < T3); V.fig.,

n " 1 - T31T2= 1 - 1 !c :y -1 = 42,6 %.2.2 .1 1 1 . " = 1 - Qced I Qab s = 1 - y P (s - 1) : [y p (e - 1) - ( y - 1)(c: - p) +

+ pl'{y-1)ln(elp)]= 9%, 17c= 1-T1IT3= 1-11c:=67%.

(s = T3 I T1, P = T3 I T2, e I P = T2 I T1). V.fig.

oa)

o

2

I

3

IIIL

II~~4

: V

4 ....-~ _" "' 3

•..· 1 - ~ " ' 2

V 0 T

p

T

2

oc)

p

2 3

c)

315



p v P

2 4 2

13

/

4 2 .' O~· ..~...~ / 4 ..&-~/ .. . ./ "'l)~ ..~~ •..•

00 V 0 T 0 Ta) b) c)

Fig.2.2.109 R

P V P

13

2 P

2P1

34

I

f,

f,/

,I , ,, - - : -

0 V 0 T 0 Ta ) b) c)

0ig.2.2.110 R

P 2 3 V 4

b)Fig.2 .2.111 R

2.2.112 . V.fig. 17= 1 - /0 2/ /01 = 1 - Cv(T3 - T~: [Cp(T2 - T1)] =

= 1 - T4(T31 T4 -1) : [yT1(T21 T1 - 1) ] = 1 - (p Y -1) : [y e y-1 (p -1)] = 53 % .

17C1=1 - T41T1 =1 -1I ey-1 =60 %, 17C2=1 - T41T2 =1 _1/( pey-1)= 80 %.

2.2.113. 17= 1 -y(T4 - T1): [T2- T1 + y(T3- T2)] = 1 -y(e -1):: [(e 1p) r - 1 + y (s 1p) y (p - 1)] = 27 %, 17c= 1 - 1 1 e = 80 %.

2.2.114.17 = 1 - [e (p 1 e) Y - e + y(e - 1)] : [1 3- 1 + yQ(p - 1)] = 27 %.T31T1 = (T3IT2) (T2IT1) =po, 17c= 1- 1 : (po ) =87 %.

2.2.115. V.fig. 2.2.108 R. L = (P2 - P1)(V3 - V1) = (PoVo 1 To) (T3 1 V3-

- T1 1 V1) (V3 ~ V1) = 45 J .

1° -- -~ -~4

o a)

316

V o

~_~- - o4I

f

T

3

oc)

P

o



2

c)

_+-...

Tc)

4

3

T

1)] =-1)]=53% .

. 1) = 80 % .

) :

=27%.

p

oa)

P

2P1 __2 [ 035P -- 6

1 11 14 11 1 11 1 11 1 11

2~ __

v P

,,4 /

0 '/ I ,

\t~ , // d'" / "" a./ / ,~-

o T oc)

Tb)

Fig.2.2 .112 R2.2.116 . '71 = ( Y - 1) : (1 + 2y), '72 =2( Y - 1) : (1 + 4 y) ,

'71/'72 = (1 + 4 y) : [2(1 +2 y)] < 1 . V.fig .

V63 V1 - - - - - " . .,--E-. . . , .

2

P

TV1 2V1 3V1 V 0 . T 0

~ ~ ~Fig.2.2 .116 R

2.2.117. '7 =1 - (T4 - T1) I (T3 - T2) =1 - T11 T2·

'7e = 1 - T1 1 T3>'7 , deoarece T3> T2. V.fig.P V P

I

14

I

. . ./2,

I I ,I ,

/

I ,,

/ /

/ , , ,

0 V 0 T 0 T

V

a) b) c)Fig.2.2.117 R

2.2.118. a) Q p = vCpAT, Cv = Cp - R = Qp/( vA T) - R = 12 ,4 J/(mol .K) .

b) AS T = vR In(V31 V2) ~ V31 V2 =exp{AS T 1 (vR)} =20 ,

Lad=- vCv(T2 - T1) ~ T1 - T2= L a d 1 (vCv) =260 K. V.fig.

317I



P \ V\

\\

31

4

s .T2 T1

10 V 0 Ta)

Giclul GARNO T inver s at

b)

p T1

T. .•2

4..Q

=o' ' isc o

3

T1 1..Q

c o Iti s

2 c o

2/

/

.: "3,~--

o T 0

Giclul GARN O T inve rsat d)Fig.2.2 .118 R

2.2 .119. F = - Po { (f - h)4 5] : [(e - h)2 - 4x 4) . x ,

F : :::: P o [4 5/ (e - h)] . x =- k x, k =45p o / (e - h) ,

1 1 fk 1 45po 1 ~v= T = 2n V - ;= 2 n (f-h)p5h =;V~ =31,8 H z.

v · =~~ fP :=20H Zrnm i t evp' .

2.3.1. T = (V / VI!) NA / N* =2,68 . 10 16 S =8,5 . 10 8 ani!

2.3.2 . L = No = [PV/(R7)] 0 = 8,2 . 10 12 km , adica de 5500 0 ori dis tantaParnant-S oare (149 ,5 . 10 6 km) . 5 = N 0 =L 0 = 2,5 km 2 .

2.3 .3. P = (m /1 ' ) RT / V = 1365 atm .2.3.4 . pV =NkT , ( k=R / N A), (N 2 - N1) : N1= (T1 - T2) : T2 = - 4,0 %.

318

c)

3. TEORIA CINETICO-MOLECULARA

s

= 2.2

2-

mmls

2

=2.

2.

2.

c =p ,

2-

2 .

c -

2 .

2.

f =

2 . 3



1T

)4

. Q

Ctl'"5C tl

3

s

ri dis tant a

= -4,0 %.

2.3 .5. u 2 =3RT I It =3pV I m =3p I p ~ u = SOOm/s .

2.3.6. n = NA· 3p: ( u v/)::: 1,0.1025 m -3 ,

p =n mo =3p 1V/ =0,467 kg/m 3 :

2.3.7. q =NA mou2/2 =NA 3kT 12, T= 3q I (3R) =33600 K .

2. 3.8. Nu. (U =v (i 12) RT= (i 12) pV) .2 .3.9 . U =vCv T =v (SR 12) T::: (S 12) PV = (S 12) P m I p =2,00 kJ .

2.3.10. u H2 : u0 2 = (1102

: ItHI 1/2=4,0

2.3 .11 . . u = (3RT I A)1/2 =SOOkm/s, u I u o = [TA : (Tcfl)]1t2 = 13S .

2.3.12 . a) Q = (ml,u)c vT1(vi2 /vil -1) =(mlp)(SRI2)(n2 -1)::: 9,35 kJ .

b) P21 P1 = T21 T1 =n 2 =4,0 ; p :::m I V, P21 P1 = 1,00 .2.3.13. Q = (mlp)RTln( V2IV1)::: (mlp)RTln n,

vT =~3RT/lt =J3Qj(m In n) = 500 m /s .

2.3.14. a) L = (1/3)mu 21n [mu 2/(3P 2V1] =2,3 kJ , b) Q =L, c) tJ .U:::O.

2.3.15. vT= (3pl p)11 2=508 m/ s , p. =pRTlp= 0,029 kg/mol .

2.3.16. a) vT = (3RT I It) 1/2= (3pV I m) 112 =200 m/ s . b) N =vNA :::

= (m I fl)NA =3,0 . 10 25 . c ) U =vCJ ::: (C vl R) pV = (S/2) pV =S3 3 J .

2 .3.1 7. II = 3RtJ .T: (vi - vi ) = 0,028 kg/mol.2 1

2.3.18. n*::: Nlm =vNAI (vp) = NAill =NA v/I(3R7) =v/I(3k7) =

=2,2 . 10 25 kg-1. n* =NA I t = 11 mo ' unde mo este masa unei mo lecul e .

2 .3.19 . vTa jVTf =JNAmr/fla ::: 14. 10 6, vTf = ~3kT/mf ~ 3,6.10 -2

mm/s. ca : I'f = S/6 , f.f =3kT ~ 4 .1O-23J .

2.3.20 . - tJ.EclEe = [mo v 2 I 2 - mo(2u - v)2 I 2] : (mov 2 12) =

= (4u v - 4u 2) I v 2 = (4u I v)(1 - u I v) ~ 4 u I v = 1,0 % , ( u « v).2.3.21. T = (2/3) It goRp I R =20 kK .

2.3 .22 . Jl = Cp :cp = [(i +2) /2] ·R : c p =28 . 10 -3 kg/mol .

2.3.23. < = 5R I (2poV ilO)=6S0 J /(kg . K) = 5poI (2p o To)

cp =vc; =910 J /(kg . K), cp = C v + Rip = tpo I (2 poTo) .

2.3.24. Cv =R: [fl.(y-1 ] =603 J /)kg · K), cp::: ycv =970 J /(kg · K).

2.3.25. Cv=R: [(y - 1) JI] = p: [(y - 1) p 7] =720 J /(kg . K) ,

Cv =y R : [(y - 1) It] =y P : [(y - 1) p 7] :::1010 J /(kg . K) .

2.3.26. Cv =Cv/p =5R 1(2/1) = (5/2) v/ 1(37) = 1000 J /(kg· K) .

2.3.27. 2H2 +0 2 =2H20 ~ tv= (2 . 3R - 3 . SR/2) : [3· (S/2)R] =- 30 % ,

tp = (2 . 4 R - 3·7 R/2) : [3 · (7/2) R] = -23,8 % .(V. problema 2 .3.28).

2.3.28. c , = L(vJ v)Cvi::: L ri Cvi' Cp::: L r{Cpi.

319

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