PARTE I – TERMOLOGIA Tópico 6

^ûplkc 1 ‛ Nlif~fíëc ~ìtglkf nc{ {ûilnc{ h nc{ içvxlnc{

646

>

^ûplkc 1 6

Xgf ncef nh kf{f th{ciqhx afht xgf {fifnf pftf c ofe~ft) gf{ eëc kce{hmxlx fdtlt c atf{kc nh pfigl~c) vxh ~hg ~fgpf gh~æilkf% Pc' tìg) ihgdtfenc'{h nh {xf{ fxif{ nh Aç{lkf) hif ghtmxijcx f ~fgpf nf hgdfifmhg hg æmxf vxhe~h nxtfe~h fimxe{ {hmxenc{ h phtkhdhx vxh hif fdtlx afklighe~h% L{{c ptcqfqhighe~h ckctthx pctvxh? f, thnxlx'{h f actíf nh kch{ëc he~th f{ gciìkxif{ nc gh~fi gh~fi h nc qlntc2 d, thnxlx'{h f pth{{ëc nc nc ft ec le~htlct nc thklplhe~h2 k, jcxqh thnxíëc nf ~he{ëc {xphta lklfi lklfi hzl{~he~h he~th c qlntc h c gh~fi2 n, c kcha lklhe~h lklhe~h nh nlif~fíëc nc gh~fi ì gflct vxh c nc qlntc2 h, c kcha lklhe~h lklhe~h nh nlif~fíëc nc qlntc ì gflct vxh c nc gh~fi%

Xg h{~xnfe~h cxqlx nh xg fe~lmc hemhejhltc nh xgf h{~tfnf nh ahttc vxh c{ ~tlijc{ nh 60 g nh kcgptlghe~c jfqlfg {lnc a lzfnc{ a lzfnc{ fc kjëc exg nlf hg vxh f ~hgphtf~xtf htf nh 60 °K% Ec nlf {hmxle~h) hg xgf fxif nh Mhcmtfalf) hih cxqlx vxh) efvxhif klnfnh) f gflct ~hgph' tf~xtf vxh xg cdoh~c nh gh~fi f~lemlx) hzpc{~c fc {ci) acl 80 °K%

C h{pfíc he~th c{ ~tlijc{ pc{{ldlil~f {xf nlif~fíëc%

Kcg h{{f{ leactgfíøh{) c h{~xnfe~h th{ciqhx kfikxift f nl{~äeklf gçel' gf he~th ncl{ ~tlijc{ nh ~thg% Vxh qfict hih hekce~tcx3 lklhe~h nh nlif~fíëc ilehft nc fíc 7 6)6 ½ 60 ‛8 °K‛6 Nfnc? kcha lklhe~h Th{cixíëc?

Th{cixíëc?

C kchﬆklhe~h nh nlif~fíëc nc gh~fi ì gflct vxh c nc qlntc% Fc {ht ghtmxijfnf ef æmxf vxhe~h) f ~fgpf nh gh~fi nlif~f gfl{ nc vxh c qlntc) {ci~fenc'{h% Th{pc{~f? n 4

ΞI 7 I0 ζ Ξκ

Kcgc? I0 7 60 g 7 60000 60 000 gg qhg? 60 000 ½ 6)6 ½ 60‛8 ½ *80 ‛ 60, I 7 60000

Qckï oæ nhqh ~ht cd{htqfnc hg {xf kf{f vxh c qlntc plthz ì gfl{ th{l{~he~h vxh c qlntc kcgxg à{ qftlfíøh{ nh ~hgphtf~xtf% [h kcickft' gc{ æmxf ahtqhe~h hg xg kcpc nh qlntc kcgxg) hih ~tlekf) gf{ l{{c eëc fkce~hkh kcg c qlntc plthz% F hzpilkfíëc pftf l{{c ì vxh? f, c kfict h{phkça lkc lkc nc plthz ì ghect vxh c nc qlntc kcgxg2 d, c kfict h{phkça lkc lkc nc plthz ì gflct vxh c nc qlntc kcgxg2 k, pftf fvxhklghe~c{ lmxfl{) c qlntc kcgxg kcgxg {cath gflct qftlfíëc nh ~hgphtf~xtf2 n, c kcha lklhe~h lklhe~h nh nlif~fíëc nc qlntc kcgxg ì ghect vxh c nc qlntc plthz2 h, c kcha lklhe~h lklhe~h nh nlif~fíëc nc qlntc kcgxg ì gflct vxh c nc qlntc plthz%

Xgf tìmxf nh fixgçelc ~hg kcgptlghe~c nh 400)0 kg f 40 °K% Vxfi c qfict) hg khe~çgh~tc{) nc {hx kcgptlghe~c f 10 °K3 Nfnc? kchalklhe~h nh nlif~fíëc ilehft nc fixgçelc 7 4)8 ½ 60 ‛8 B ‛6

Th{cixíëc?

Pct~fe~c? I 7 I0 " I I 7 400)0 " 0)4 *kg,

C vxh ptcqckf c ~tlekfghe~c nc kcpc ì c af~c nh vxh f pfthnh le~ht' ef *vxh he~tf hg kce~f~c kcg f æmxf vxhe~h, nlif~f'{h gfl{ nc vxh f pfthnh hz~htef% Kcgc c kchﬆklhe~h nh nlif~fíëc nc qlntc kcgxg ì gflct nc vxh c nc qlntc plthz) ì gfl{ aækli c qlntc kcgxg ~tlekft% Th{pc{~f? h ;

I 7 >)> gg

Th{pc{~f? >)> gg 8

Th{cixíëc?

ΞI 7 I0 ζ Ξκ

I 7 400)0 ½ 4)8 ½ 60‛8 ½ *10 ‛ 40, *kg, I 7 0)4 kg

I 7 400)4 kg Th{pc{~f? 400)4 kg 1

H%T%

Xgf dfttf nh kcdth) jcgcmïehf h xelactgh) ghnh 40 g) f 0 °K% Kfikxih f qftlfíëc nc kcgptlghe~c nh{{f dfttf) hg gl' içgh~tc{) vxfenc fvxhklnf f 80 °K% Nfnc? kchalklhe~h nh nlif~fíëc ilehft nc kcdth 7 6)1 ½ 60 ‛8 °K‛6 Th{cixíëc? X{fenc f hvxfíëc nf nlif~fíëc ilehft) ~hgc{?

ΞI 7 I0 ζ Ξκ

[xd{~l~xlenc c{ qficth{ actehklnc{) qhg? ΞI 7 40 ½ 6)1 ½ 60‛8 ½ *80 ‛ 0, ΞI 7 0)061 g 7 61 gg ΞI 7 61 gg

À ~hgphtf~xtf nh 0 °K) xg alc nh kcdth ghnh 600)000 g% [hx kcgptlghe~c pf{{f f {ht nh 600)01: g vxfenc f ~hgphtf~xtf f~lemh >0 °K% Vxfi c qfict nc kchalklhe~h nh nlif~fíëc ilehft nc kcdth3 Th{cixíëc?

ΞI 7 I0 ζ Ξκ ζ7

I I0 κ

F{{lg? 600)01: ‛ 600)00 ζ 7 600)000 ½ *>0 ‛ 0, *°K‛6, 0)01: ‛6 *°K , ζ7 > 000  7 6)= ½ 60‛8 °K‛6

Th{pc{~f? 6)= ½ 60‛8 °K‛6

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644

PFT^H L ‛ ^HTGCICMLF

=

*Xhpf ‛ gcn%, C{ ~tlijc{ nh ~thg) ectgfighe~h nh 40 g nh kcg' ptlghe~c) {ëc kcickfnc{ nh gcnc f gfe~ht he~th nxf{ pce~f{ kce{h' kx~lqf{ xgf phvxhef acimf kjfgfnf oxe~f nh nlif~fíëc% L{{c hql~f vxh hih{ {h h{pthgfg) {cathenc nhactgfíøh{ nhqlnc à fíëc nc kfict ec{ nlf{ vxhe~h{%

Kce{lnhth vxh xgf qftlfíëc nh ~hgphtf~xtf nf ecl~h pftf c *ghlc, nlf pc{{f kjhmft f *fptczlgfnfghe~h, 48 °K) afhenc'c{ nlif~ft khtkf nh 8 gg% Eh{~h kf{c) vxfi c qfict nc kcha lklhe~h kcha lklhe~h nh nlif~fíëc ilehft nc gf~htlfi nh vxh ì ahl~c c ~tlijc3 Th{cixíëc? I I0 κ 8 ‛6 ζ 7 40 40000 000 ½ 48 *°K ,

ζ7

 7 6)0 ½ 60‛8 °K‛6

60

Xgf dfttf gh~æilkf nh kcha lklhe~h lklhe~h nh nlif~fíëc ilehft gìnlc nh ‛6 4 ½ 60 °K f 40 °K ì kcickfnf ec le~htlct nh xg actec% Fpû{ f dfttf ~ht f~lemlnc c hvxliçdtlc ~ìtglkc) qhtlalkf'{h vxh {hx kcgptlghe~c ì 6( gflct% Vxfi f ~hgphtf~xtf nc actec3 ‛8

Th{cixíëc?

I0 ↔ 600( I ΞI ↔ 6( ⇔ ΞI 7 0 600 Kcgc? ΞI 7 I0 ζ Ξκ) he~ëc? I0 600 7 I0 ζ Ξκ 6 ‛8 600 7 4 ½ 60 *κ ‛ 40, 800 κ6 ‛ 40 ⇔

Th{pc{~f? κ6 7 840 °K 66

F a lmxtf lmxtf fdflzc thpth{he~f c kcgptlghe~c nh xgf dfttf gh~æ' ilkf hg axeíëc nh {xf ~hgphtf~xtf% I *kg,

Th{pc{~f? 6)0 ½ 60‛8 °K‛6

600)4

:

*XHI'PT, Xgf dfttf gh~æilkf) lelklfighe~h à ~hgphtf~xtf nh 40 °K) ì fvxhklnf f~ì 410 °K h {cath xgf nlif~fíëc lmxfi f 0)1( nh {hx kcgptlghe~c lelklfi% Vxfi c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft gìnlc nc gh~fi eh{{h le~htqfic nh ~hgphtf~xtf3 Th{cixíëc?

I0 ↔ 600(

0)1 I0 ΞI ↔ 0)1( ⇔ ΞI 7 600 Kcgc? ΞI 7 I0 ζ Ξκ) he~ëc? 0)1 ½ I0 7 I0 ζ Ξκ 600 1 ½ 60‛; 7 ζ ½ *410 ‛ 40, ζ 7 4)8 ½ 60 ‛8 °K‛6 Th{pc{~f? 4)8 ½ 60‛8 °K‛6

κ6 7 840 °K

600)0

0

80 ~ *°K,

Vxfi c qfict nc kchalklhe~h nh nlif~fíëc ilehft nc gf~htlfi nh{{f dfttf3 Th{cixíëc?

ΞI 7 I0 ζ Ξκ

600)4 ‛ 600)0 7 600)0 ½ ζ ½ *80 ‛ 0, 0)4 7 8000 8 000 ½ ζ ζ 7 >)0 ½ 60‛8 °K‛6 Th{pc{~f? >)0 ½ 60‛8 °K‛6 64

C nlfmtfgf fdflzc gc{~tf f qftlfíëc ΞI {catlnf pct xgf dfttf gh~æilkf nh kcgptlghe~c lelklfi lmxfi f 60 g hg axeíëc nf qftlfíëc nh ~hgphtf~xtf Ξκ%Vxfi c qfict nc kchalklhe~h nh nlif~fíëc ilehft nc gf~h' tlfi nh{{f dfttf3 ΞI *gg,

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Xg a lc lc nh kcdth) kcg 6)000 g nh kcgptlghe~c f 40 °K) acl kcic' kfnc hg xg actec) nlif~fenc'{h f~ì f~lemlt 6 064 gg% Vxfi ì f ~hgph' tf~xtf nc actec) {xpc{~f kce{~fe~h3 Nfnc? kchalklhe~h nh nlif~fíëc ilehft nc kcdth 7 6)1 ½ 60 ‛8 °K‛6

61

Th{cixíëc? I 7 I0 ζ κ

6 064 ‛ 6000 6 000 7 6000 6 000 ½ 6)1 ½ 60‛8 ½ *κa ‛ 40, 64 7 6)1 ½ 60‛4 *κ ‛ 40,

0

Th{cixíëc?

600 60 0 Ξκ *°K,












6;

*Xelif{fiih, Hg xgf hzphtlïeklf pftf ghnlt c kchalklhe~h nh nl' if~fíëc ilehft gìnlc nh xg phnfíc nh gh~fi nh{kcejhklnc) cd~hqh'{h c {hmxle~h mtæa lkc lkc nc kcgptlghe~c hg axeíëc nf ~hgphtf~xtf? I *kg,

64;

Th{cixíëc?

Kcickfenc'{h æmxf atlf ec kcpc le~htec h ghtmxijfenc'{h c kcpc hz' ~htec hg æmxf vxhe~h) c hz~htec nlif~f'{h h c le~htec kce~tfl'{h) ckct' thenc f {hpftfíëc he~th hih{% Th{pc{~f? n

80)0=0

68

H%T %T%%

Xgf ~thef nh fixgçelc acl mtfnxfnf kctth~fghe~h f xgf ~hgphtf~xtf nh ;0 °K) vxfenc {hx kcgptlghe~c ~c~fi fpth{he~cx 80)000 g% H{{f ~thef pc{{xl mtfnxfíëc f~ì c gliçgh~tc% Vxfi f gæzl' gf nl{~äeklf vxh f ~thef ì kfpf nh ghnlt) hg xg ickfi cenh f ~hg' phtf~xtf fgdlhe~h ì ‛40 °K3 Nfnc? kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc fixgçelc 7 4> ½ 60 ‛1 °K‛6

80)0;8

Th{cixíëc?

80)000 40

10

600 ^ *°K,

Fdflzc {hmxh xgf ~fdhif kcg c{ kchalklhe~h{ nh nlif~fíëc ilehft gì' nlf) ) pftf fimxe{ gh~fl{? Gh~fi

*°K‛6,

Fíc

66 ½ 60‛1

Cxtc

6>); ½ 60‛1

Kcdth

6=)0 ½ 60‛1

Fixgçelc

4;)0 ½ 60‛1

Kjxgdc

4<)0 ½ 60‛1

Kfikxifenc'{h c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft f pft~lt nc{ nfnc{ hzphtlghe~fl{ *mtæalkc,) leahtlgc{ vxh c gh~fi hg vxh{~ëc {h ~tf~f ptcqfqhighe~h nc? f, kjxgdc2 n, cxtc2 d, fixgçelc2 h, fíc% k, kcdth2

Kjfghgc{ nh x 0 f xelnfnh hg gh~tc{ ef ~hgphtf~xtf f vxh f ~thef acl mtfnxfnf h nh x f xelnfnh) ~fgdìg hg gh~tc{) f xgf ~hgphtf' ~xtf vxfivxht% Cd{htqhgc{ vxh) {h hihqftgc{ f ~hgphtf~xtf nf ~thef) hif {h nl' if~ftæ h x 5 x 02 pctìg) {h nlglexltgc{ f ~hgphtf~xtf) f ~thef {h kce~tfltæ h x 9 x 0 % X{fenc f hzpth{{ëc nf nlif~fíëc ilehft? x 7 x0*6 " ζΞκ, h {henc x0 f xelnfnh kctth~f *{hx qfict ì 6)000 g,) ~hgc{? x 7 6)000 ½ R6 " 4> ½ 60‛1 *‛80,W x 7 6)000 ½ R6 ‛ 0)0064W x 7 0)<<:: g À ~hgphtf~xtf nh ‛40 °K) nhqlnc à kce~tfíëc nc fixgçelc) f nl{~äeklf he~th nxf{ gftkf{) vxh f ;0 °K htf 6)000 g) pf{{f f {ht 0)<<:: g% Kcgc f ~thef pc{{xl 80 le~htqfic{ nh gh~tc) pcnhgc{ faltgft vxh f gæzlgf nl{~äeklf pc{{çqhi nh {ht ghnlnf kcg h{{f ~thef) f ‛40 °K) ì? _ 7 80x 7 80 ½ 0)<<:: _ 7 ><)<> g

Th{cixíëc?

ΞI 7 I0 ζ Ξκ

80)0=0 ‛ 80)000 7 80)000 ζ *600 ‛ 40, ⇔ 0)0=0 7 80)000 ζ :0 61

ζ 7 6)=8 ½ 60‛8 K‛6 ⇔

ζ 7 6=)8 60‛1 K‛6

C kcha lklhe~h lklhe~h nh nlif~fíëc cd~lnc) thif~lqfghe~h à ~fdhif actehklnf) ì ptcqfqhighe~h nc gh~fi kcdth% Th{pc{~f? k 6>

*Cilgpçfnf Pfxil{~f nh Aç{lkf, Ì gxl~c kcgxg fkce~hkht) vxfe' nc kcpc{ lmxfl{ {ëc hgplijfnc{ kcickfenc'{h xg nhe~tc nc cx~tc) nh ncl{ nhih{ alkfthg hgphttfnc{) ~ctefenc'{h nlaçkli {hpftæ'ic{% Kce{l' nhtfenc c hahl~c nf nlif~fíëc ~ìtglkf) pcnh'{h fa ltgft fa ltgft vxh ì pc{{çqhi th~ltft xg kcpc nh nhe~tc nc cx~tc {h? f, c{ kcpc{ hgphttfnc{ acthg ghtmxijfnc{ hg æmxf æmxf dhg vxhe~h% d, ec kcpc le~htec act nh{phofnf æmxf vxhe~h h c kcpc hz~htec act ghtmxijfnc hg æmxf dhg atlf%

*Gfkb'[P, Exg ifdctf~ûtlc) xg fixec fvxhkh nh 80 °K xgf dft' tf gh~æilkf nh kcgptlghe~c lelklfi :0 kg) cd{htqfenc vxh c {hx kcg' ptlghe~c fxghe~f nh 0): gg% Afhenc c{ kæikxic{) hih kcekixl vxh c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc gf~htlfi nf dfttf qfih? f, 8 ½ 60‛8 °K‛6% n, 4 ½ 60‛8 °K‛6% ‛8 ‛6 d, > ½ 60 °K % h, 6 ½ 60‛8 °K‛6% k, ; ½ 60‛8 °K‛6% Th{cixíëc?

ΞI 7 I0 ζ Ξκ

Kcgc? I0 7 :0 kg 7 :00 gg ~hgc{?











64>


6=

*Xel{f'[P, Xgf ilejf aìtthf ~hg ;00 bg nh hz~he{ëc ec leqhtec) vxfenc f ~hgphtf~xtf ì ‛8 °K% Pctìg) ec qhtëc) f ~hgphtf~xtf kjhmf f 48 °K% [h c{ ~tlijc{ {ëc kce{~txçnc{ nh xg gf~htlfi nh kcha lklhe~h kcha lklhe~h nh ‛8 ‛6 nlif~fíëc ilehft ζ 7 60 °K ) vxfi ì f qftlfíëc nh kcgptlghe~c vxh c{ ~tlijc{ {cathg ef {xf hz~he{ëc3 f, 60 g% k, <0 g% h, 400 g% d, 40 g% n, 680 g%

*ΞI#I0, 0)04> 0)064

6)0 ½ 60;

4)0 ½ 60; Ξκ *°K,

Th{cixíëc?

ΞI 7 I0 ζ Ξκ ΞI 7 ;00000 ;00 000 ½ 60‛8 ½ R48 ‛ *‛8,W

Th{cixíëc?

ΞI 7 I0 ζ Ξκ ΞI 7 ζ Ξκ

ΞI 7 <0 g Th{pc{~f? k 6:

[fdhenc vxh c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft gìnlc nc kce' ‛1 ‛6 kth~c ì 64 ½ 60 °K ) h{~lgh f qftlfíëc fexfi nf fi~xtf nh xg ptìnlc nh 60 fenfth{ hg xgf klnfnh nc il~ctfi nh [ëc Pfxic) xgf thmlëc ~hgph' tfnf) nhqlnc à qftlfíëc nh ~hgphtf~xtf he~th c leqhtec h c qhtëc% Th{cixíëc?

ΞI 7 I0 ζ Ξκ

Pct h{~lgf~lqf) ~hgc{? I0 60 ½ ; g ;0 g Ξκ 40 °K 

I 7 606): kg



Th{pc{~f? 606): kg



Pct~fe~c? ΞI ;0 ½ 64 ½ 60‛1 ½ 40 *g,

46



ΞI



=)4 ½ 60‛; g ⇔

ΞI



=)4 gg

Th{pc{~f? =)4 gg 6<

Bhqle) xg hemhejhltc fghtlkfec) acl kceqlnfnc pftf ptcoh' ~ft {cdth xg tlc xgf pce~h gh~æilkf kcg 4)0 bg nh kcgptlghe~c% Eh{{f thmlëc) f fgpil~xnh fexfi nh ~hgphtf~xtf{ qfl nh fptczlgfnf' ghe~h ‛>0 °A f~ì 660 °A% C kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc gf~htlfi ‛1 ‛6 nf pce~h ì 64 ½ 60 °K % Kce{lnhtfenc c{ hahl~c{ nh kce~tfíëc h hz' pfe{ëc ~ìtglkf nc gh~fi nf pce~h) vxfi f gæzlgf qftlfíëc h{phtfnf hg {xf hz~he{ëc3 Th{cixíëc?

ΞI 7 I0 ζ Ξκ

[henc? I0 7 4)0 bg 7 4 000 g Ξκ 7 R660 ‛ *‛>0,W °A 7 680 °A Kcgc? ΞκK

I0 0)04> 7 ζ 4)0 ½ 60; ζ 7 6)4 ½ 60‛8 °K‛6 Pct~fe~c? ΞI 7 I0 ζ Ξκ 6 800 *kg, ΞI 7 600)0 ½ 6)4 ½ 60‛8 ½ 6800 ΞI 7 6): kg Kcgc? I 7 I0 " ΞI) he~ëc? I 7 600)0 " 6):

Ξκ ΞκK 680 7 A ⇔ 7 7 480 °K) 600 6:0 600 6:0 ⇔ ΞκK ; he~ëc? ΞI 7 4)0 g 4 000 ½ 64 ½ 60‛1 ½ 480 ΞI 7 4000 ; *g, ⇔ Th{pc{~f? 4)0 g

*XAPL, F nlahtheíf he~th c{ kcgptlghe~c{ nh nxf{ dfttf{ gh~æ' ilkf{ {h gfe~ìg kce{~fe~h) hg :0)0 kg) exg le~htqfic nh ~hgphtf~xtf hg vxh qfih f fptczlgfíëc ilehft pftf f nlif~fíëc% C{ kcha lklhe~h{ kcha lklhe~h{ nh nlif~fíëc ilehft f{{cklfnc{ à{ dfttf{ {ëc ;)0 ½ 60 ‛8 °K‛6 h 4)0 ½ 60‛8 °K‛6% F{{lg) pcnhgc{ nlht vxh) à ~hgphtf~xtf lelklfi) f{ dfttf{ ghnlfg? f, 4)> g h 6)1 g% n, >)0 g h ;)4 g% d, 4)8 g h 6)= g% h, >)> g h ;)1 g% k, ;)4 g h 4)> g% Th{cixíëc?

Kcenlíëc? ΞI6 7 ΞI4 I0 ζ6 κ 7 I0 ζ4 κ 6

4

I0 ½ ;)0 ½ 60‛8 7 *I0 " 0):0, ½ 4)0 60‛8 6

6

;)0I0 7 4)0I0 " 6)1 6

6

I0 7 6)1 g 6

I0 7 I0 " 0):0 4

6

I0 7 6)1 " 0):0 4

I0 7 4)> g 4

Th{pc{~f? f 44

*Gfkb'[P, Nxf{ dfttf{ F h D nh gh{gc gf~htlfi ~ïg f 0 °K kcg'












Th{cixíëc?

ΞI 7 I0 ζ Ξκ

Kcgc f{ dfttf{ {ëc nh gh{gc gf~htlfi * ζF 7 ζD 7 ζ, h {cathtfg c gh{' gc fvxhklghe~c * ΞκF 7 ΞκD 7 Ξκ,) ~hgc{? ΞI 7 ζ Ξκ2 I0 I0 ΞI ΞI ΞI D he~ëc? ΞI F 7 ΞI D ⇔ ΞIF 7 I 0F 0D D 0D 0); ΞID 7 0)>0 kg 7 0)=8 ⇔ ΞID Th{pc{~f? f 4;

648

he~ëc? I0 ζAh Ξκ 7 I0 ζkcek Ξκ Ah kcek *=): ‛ j, 6; ½ 60‛1 7 =): ½ 64 ½ 60‛1 6;*=): ‛ j, 7 =): ½ 64 6; ½ =): ‛ 6; j 7 64 ½ =): j 7 0)10 g

=): 7 6; j ⇔ Th{pc{~f? 0)10 g 48

F a lmxtf lmxtf gc{~tf xgf phvxhef h{ahtf hg thpcx{c {cdth f dfttf jctlce~fi) {x{~he~fnf pct ncl{ a lc{ lc{ gh~æilkc{ nh gf~htlfl{ nlahthe~h{ 6 h 4) nh kcgptlghe~c{ nh{lmxfl{ I 6 h I4) f 0 °K%

H%T %T%%

*AHL'[P ‛ gcn%, F{ dfttf{ F h D nf a lmxtf lmxtf ~ïg) th{phk~l' qfghe~h) 6 000 gg h 6 006 gg nh kcgptlghe~c f 40 °K% [hx{ kch' a lklhe~h{ lklhe~h{ nh nlif~fíëc ilehft {ëc? ζF 7 ;)0 ½ 60‛8 °K‛6 h ζD 7 6)0 ½ 60‛8 °K‛6%

*6,

*4,

K

F

D

Vxfi ì f ~hgphtf~xtf hg vxh f dfttf K a lkftæ lkftæ ef pc{líëc jctlce~fi3 Th{cixíëc?

Vxfenc f dfttf K h{~lqht ef jctlce~fi) c{ kcgptlghe~c{ nf{ dfttf{ F h D {htëc lmxfl{? IF 7 ID Kcgc? I 7 I0 *6 " ζ Ξκ,) ~hgc{? I0 *6 " ζF Ξκ, 7 I0 *6 " ζD Ξκ, F

D

6 000 ½ *6 " ;)0 ½ 60‛8 ½ Ξκ, 7 6006 6 006 ½ *6 " 6)0 ½ 60‛8 ½ Ξκ, ‛8 6 000 " ; 000 ½ 60 ½ Ξκ 7 6006 6 006 " 6006 6 006 ½ 60‛8 ½ Ξκ ‛8 6<<< ½ 60 Ξκ 7 6 Ξκ 80 °K κ ‛ 40 80

[henc ζ6 h ζ4 c{ th{phk~lqc{ kchalklhe~h{ nh nlif~fíëc ilehfth{ nc{ alc{ *6, h *4,) vxfi nf{ thifíøh{ f {hmxlt thpth{he~f f kcenlíëc pftf vxh f dcif kce~lexh hvxlildtfnf {cdth f dfttf) fc qftlft f ~hgphtf~xtf3 f, ζ6 7 ζ4 k, ζ6 I4 7 ζ4 I6 h, I4 7 I6 ζ6 ζ4 d, ζ6 I6 7 ζ4 I4 n, I6 I4 7 ζ6 ζ4 Th{cixíëc?

Kcenlíëc? ΞI6 7 I4 he~ëc? I6 ζ6 Ξκ 7 I4 ζ4 Ξκ ζ6 I6 7 ζ4 I4 Th{pc{~f? d





κ



=0 °K

41

H{~ëc thpth{he~fnc{) f {hmxlt) c{ kcgptlghe~c{ nh nxf{ dfttf{

F h D hg axeíëc nf ~hgphtf~xtf? D

I

F

4>

Xgf pif~factgf P acl fpclfnf hg nxf{ kcixef{) kceactgh f a lmxtf lmxtf f {hmxlt? P

Th~f{ pftfihif{

6)8  6)0  0

κ

Nh~htgleh f tfëc he~th c{ kchalklhe~h{ nh nlif~fíëc ilehft nh{{f{ dfttf{% j

Nhqlnc f xg nh{eçqhi nc ~htthec) pftf gfe~ht f pif~factgf {hgpth ef jctlce~fi f vxfivxht ~hgphtf~xtf) acl pthkl{c afht xgf nf{ kcixef{ nh kcekth~c h f cx~tf nh ahttc% Vxfi c qfict nc nh{eçqhi j) {fdhenc'{h vxh f gflct kcixef ì nh kcekth~c h ghnh =): g f 0 °K3 Nfnc{?

‛1

‛6

Th{cixíëc?

ΞI ~m f 7 Ξκ 7 I0 ζ he~ëc? ~m f 7 I 0 ζ Kcgc f{ th~f{ {ëc pftfihif{? ~m fF 7 ~m fD

I

f

κ











641


4=

Kce{lnhth ~tï{ dfttf{ gh~æilkf{ jcgcmïehf{ F) D h K% C mtæalkc f {hmxlt thpth{he~f c kcgptlghe~c nf{ dfttf{ hg axeíëc nf ~hgphtf~xtf% I >f

Dfttf K Dfttf D

f, Pd) F) Ah2 d, F) Pd) Ah2 k, Ah) Pd) F2

n, F) Ah) Pd2 h, Ah) F ) Pd%

Th{cixíëc?

Ec nlfmtfgf) ~hgc{?

;f 4f Dfttf F

f 0

Ξ

κ

d

f

C{ kcha lklhe~h{ lklhe~h{ nh nlif~fíëc ilehft nf{ dfttf{ F) D h K qfihg) th{phk~l' qfghe~h) ζF) ζD h ζK% F thifíëc he~th ζF) ζD h ζK ì? f, ζF 7 ζD 7 ζK% n, ζF 7 ζK 7 4ζD% d, ζF 7 ζD 7

ζK

%

h, ζF 7 ζK 7

4 k, ζF 7 ζD 7 4ζK%

ζD

4

%

Ξκ

~m f 7 ΞΞκ F{{lg) nf ~fdhif) qhg? ~m fAh 7 ΞΞκ

Th{cixíëc?

ΞI 7 I0 ζ Ξκ

7 0)10 kg 7 6)4 ½ 60‛; kg#°K 800 °K Ah

~m fFi 7 ΞΞκ 7 0)>1 kg 7 4); ½ 60‛; kg#°K 400 °K Fi

Pftf f dfttf F? *4f ‛ f, 7 f ζF*d ‛ 0, f 7 f ζF d ⇔ ζF 7 6 d Pftf f dfttf D? *;f ‛ 4f, 7 4f ζD *d ‛ 0, f 7 4f ζD d ⇔ 4 ζD 7 6 d He~ëc? ζF 7 4ζD Pftf f dfttf K? *>f ‛ 4f, 7 4f ζK *d ‛ 0, 4f 7 4f ζK d ⇔ ζK 7 6 d Pct~fe~c?

~m fPd 7 ΞΞκ

7 0)4= kg 7 4)= ½ 60 ‛; kg#°K 600 °K Pd

Kcgc? ~m fPd  ~m fFi  ~m fAh he~ëc? fPd  fFi  fAh Pct~fe~c) f kctthifíëc he~th f{ th~f{ h c{ gf~htlfl{ ì? F ↔ Kjxgdc *Pd, D ↔ Fixgçelc *Fi, K ↔ Ahttc *Ah,

ζF 7 ζK 7 4ζD Th{pc{~f? n

Th{pc{~f? f

4:

4<

C mtæa lkc lkc nf a lmxtf lmxtf f {hmxlt gc{~tf f nlif~fíëc ~ìtglkf nh ~tï{ dfttf{ gh~æilkf{) ahl~f{ nh fixgçelc *F ,) ahttc *Ah, h kjxgdc *Pd,% C fvxhklghe~c ì ahl~c f pft~lt nh 0 °K) h hif{ pc{{xhg c gh{gc kcgptl' ghe~c lelklfi% F ~fdhif gc{~tf ~fgdìg fimxe{ nfnc{ exgìtlkc{ thah' the~h{ fc ptckh{{c%

H%T %T%%

Nxf{ dfttf{ F h D) nh kcha lklhe~h{ lklhe~h{ nh nlif~fíëc ilehft ζF h ζD h kcgptlghe~c{ IF h ID) {ëc hghenfnf{ nh gcnc vxh kce{~l~xf xgf ÿelkf dfttf nh kcgptlghe~c *I F " I D,% Vxfi ì c kchalklhe~h nh nlif~fíëc ilehft nh{{f ecqf dfttf3 Th{cixíëc?

C kchalklhe~h nh nlif~fíëc ilehft nh xgf dfttf ì nfnc phif hzpth{{ëc? ζ 7 ΞI I0 Ξκ Hg xg fvxhklghe~c Ξκ vxfivxht) ~hgc{?

*kg, F D K

ΞIF 7 IF ζF Ξκ ΞID 7 ID ζD Ξκ

0

ΞI 7 I0 ζ Ξκ 0

*°K,

Ξ *kg,

Ξκ *°K,

Pct~fe~c? I ζ Ξκ " ID ζD Ξκ ΞIF " ΞID 7 F F ζ 7 ΞI 7 I0 Ξκ *IF " ID, Ξκ *IF " ID, Ξκ I

"I














;0

*XHI'PT, F dfttf nf almxtf ì kcgpc{~f nh ncl{ {hmghe~c{? xg nh kcgptlghe~c h kcha lklhe~h lklhe~h nh nlif~fíëc ilehft ζF h cx~tc nh kcg' ptlghe~c 4  h kchalklhe~h nh nlif~fíëc ilehft ζD% Pcnh'{h fa ltgft ltgft vxh c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nh{{f dfttf) ) ì lmxfi f? 

f,

ζF " ζD

d,

4ζF " ζD % ;

%

4

;;

*XAGM, Xgf iäglef dlgh~æilkf ì kce{~l~xlnf nh nxf{ pifkf{ nh gf~htlfl{ nlahthe~h{) G6 h G4) pth{f{ xgf à cx~tf% H{{f iäglef pcnh {ht x~lilfnf kcgc le~httxp~ct ~ìtglkc pftf ilmft cx nh{ilmft xg kltkxl~c hiì~tlkc) kcgc thpth{he~fnc) h{vxhgf~lkfghe~h) ef a lmxtf lmxtf L?

4

F

Iäglef dlgh~æilkf

D

ζF " 4ζD

k,

;

%

Kce~f~c

h, ;*ζF " ζD,%

Kltkxl~c hiì~tlkc L Iäglef dlgh~æilkf

Th{cixíëc?

ΞIdfttf 7 ΞIF " ΞID

Kce~f~c

D

Kltkxl~c hiì~tlkc

I0 " I0 ζdfttf 7 I0 ζF " I0 ζD F

D

F

D

* " 4,ζdfttf 7 ζF " 4 ζD ; ζdfttf 7  *ζF " 4ζD, ζdfttf 7

ζF " 4ζD

;

LL

Vxfenc f ~hgphtf~xtf nf{ pifkf{ fxghe~f) hif{ nlif~fg'{h h f iäglef kxtqf'{h) ahkjfenc c kltkxl~c hiì~tlkc) kcgc gc{~tfnc ef al mxtf LL% H{~f ~fdhif gc{~tf c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nh nlahthe~h{ gf~htlfl{? Gf~htlfi

Th{pc{~f? k ;6

^tï{ df{~øh{ nh gh{gc kcgptlghe~c ) xg nh fixgçelc *ζFi 7 4> ½ 60‛1 °K‛6,) cx~tc nh if~ëc * ζif~ëc 7 40 ½ 60‛1 °K‛6, h c ~htkhltc nh kcdth *ζKx 7 61 ½ 60 ‛1 °K‛6,) {ëc hghenfnc{ nh gcnc vxh kce{~l~xfg xg ÿelkc df{~ëc nh kcgptlghe~c ; % Nh~htgleh c kcha lklhe~h lklhe~h nh nlif' ~fíëc ilehft nc df{~ëc th{xi~fe~h% Th{cixíëc?

ΞIdf{~ëc 7 ΞIF " ΞIif~ëc " ΞIKx ;Iζdf{~ëc Ξκ 7 IζF Ξκ " Iζif~ëc Ξκ " I ζKx Ξκ ζdf{~ëc 7

ζF " ζif~ëc " ζKx

; ‛1 ‛1 10 ½ 60‛1 ζdf{~ëc 7 4> ½ 60 " 40 ½ 60 " 61 ½ 60 7 ; ; ‛1

ζdf{~ëc 7 40 ½ 60‛1 °K‛6

G4 G6

I0 ζdfttf ½ Ξκ 7 I0 ζF Ξκ " I0 ζD Ξκ F

G4 G6

n, ζF " 4ζD%

dfttf

64=

ζ *60‛1 ½ °K‛6,

Fíc

66

Fixgçelc

4>

Dtcezh

6<

Kcdth

6=

Eçvxhi

6;

Kce{lnhth vxh c gf~htlfi G6 ì kcdth h c cx~tc) G 4) nhqh {ht h{kcijlnc he~th c{ il{~fnc{ eh{{f ~fdhif% Pftf vxh c kltkxl~c {hof ilmfnc kcg c ghect fxghe~c nh ~hgphtf~xtf) c gf~htlfi nf iäglef G 4 nhqh {ht c? f, fíc% d, fixgçelc% k, dtceh% n, eçvxhi% Th{cixíëc?

Pftf vxh f iäglef {h kxtqh kcg c ghect fxghe~c nh ~hgphtf~xtf) f iäglef G4 nhqhtæ ~ht c gflct kchalklhe~h nh nlif~fíëc *c fixgçelc,%











64:


;8

*Cilgpçfnf Dtf{lihltf nh Aç{lkf, F a lmxtf lmxtf lix{~tf xgf phíf nh gh~fi kcg xg ctlaçklc nh nlägh~tc n 6 h xg plec nh nlägh~tc n4 ilmhl' tfghe~h gflct vxh c ctlaçklc n 6) vxfenc à gh{gf ~hgphtf~xtf% Pftf le~tcnxlt c plec ec ctlaçklc) pcnh'{h? n6 f, fvxhkht fgdc{? fgdc{? c ctlaçklc h c plec% d, th{atlft c plec% k, fvxhkht c plec h th{atlft c ctlaçklc% n4 5 n6 n, th{atlft c ctlaçklc% h, th{atlft fgdc{? c ctlaçklc h c plec%

~hgc{? 0)06F0 7 F0 48 ½ 60‛1 *κ ‛ 40, >00 7 κ ‛ 40 ⇔

κ 7 >40 °K

;<

À ~hgphtf~xtf nh 68 °K) hekce~tfgc{ xgf kjfpf nh kcdth kcg {xphtaçklh nh æthf 600)0 kg4% Vxh æthf ~htæ h{{f {xphtaçklh {h f kjfpf act fvxhklnf f~ì 868 °K3 lklhe~h nh nlif~fíëc {xphtalklfi nc kcdth 7 ;)4 ½ 60 ‛8 °K‛6 Nfnc? kcha lklhe~h

Th{cixíëc?

Pftf vxh c plec pc{{f {ht le~tcnxlnc ec ctlaçklc) pcnhgc{ fvxhkht c ctlaçklc h#cx th{atlft c plec% Th{pc{~f? d ;1

C{ gf~htlfl{ x{fnc{ pftf f cd~xtfíëc nh nhe~h{ h c{ nhe~h{ pc{{xhg kchalklhe~h{ nh nlif~fíëc ~ìtglkf nlahthe~h{% F{{lg) nc pce~c nh ql{~f aç{lkc) pct vxh pcnh {ht pthoxnlklfi fc{ nhe~h{ lemhtltgc{ dh' dlnf{ gxl~c vxhe~h{ cx gxl~c mhifnf{3 Th{pc{~f? [h f cd~xtfíëc nlif~ft gfl{) c nhe~h pcnh vxhdtft% [h

nlif~ft ghec{) pcnhg ckcttht leali~tfíøh{%

Th{cixíëc?

ΞF 7 F0 δ Ξκ ΞF 7 600)0 ½ ;)4 ½ 60‛8 ½ *868 ‛ 68, ΞF 7 6)1 kg 4

Pct~fe~c? F 7 F0 " F F 7 600)0 " 6)1 *kg4, F 7 606)1 kg4 Th{pc{~f? 606)1 kg4 >0

Xgf {xd{~äeklf ~hg kcha lklhe~h lklhe~h nh nlif~fíëc {xphta lklfi lklfi F h kcha lklhe~h lklhe~h nh nlif~fíëc qcixgì~tlkf D% F{{lg) c kcha lklhe~h lklhe~h nh nlif~f' íëc ilehft ì lmxfi f? f, 4F% d, D % k, F % n, FD % h, ;FF % 4 ; 1 >D

Hg xgf pifkf nh cxtc) jæ xg phvxhec ctlaçklc) vxh f ;0 °K ~hg {xphtaçklh nh æthf 8 ½ 60 ‛; kg4% F vxh ~hgphtf~xtf nhqhgc{ ihqft h{{f pifkf pftf vxh f æthf nc ctlaçklc fxghe~h c kctth{pcenhe~h f 1 ½ 60‛8 kg43 lklhe~h nh nlif~fíëc ilehft nc cxtc 7 68 ½ 60 ‛1 °K‛6 Nfnc? kcha lklhe~h

Th{cixíëc?

Th{cixíëc?

^hgc{? δ7F λ 7 D

ΞF 7 F0 δ Ξκ ΞF 7 F0 4ζ Ξκ

;=

ζ7

δ

4

7

1 ½ 60‛8 7 8 ½ 60‛; ½ 4 ½ 68 ½ 60‛1 ½ *κa ‛ ;0, >00 7 κa ‛ ;0 λ

;

F 7 4ζ D 7 ;ζ F{{lg) qhtla lkfenc lkfenc f{ th{pc{~f{) ~hgc{? ;FF 7 ;*4ζ, *4ζ, 7 ζ >D > *;ζ,

κa 7 >;0 °K Th{pc{~f? >;0 °K >6

H%T %T%%

Hg xgf kjfpf nh if~ëc) f 0 °K) ah'{h xg ctlaçklc kltkxift nh 40)0 kg nh nlägh~tc% Nh~htgleh c fktì{klgc nh æthf vxh c ctlaçklc {cath vxfenc f ~hgphtf~xtf nf kjfpf ì hihqfnf f 480 °K% Nfnc? kchalklhe~h nh nlif~fíëc ilehft nc if~ëc 7 4 ½ 60 ‛8 °K‛6












>4

*XAX'GM ‛ gcn%, Xg ctlaçklc exgf pfehif nh ahttc) f 40 °K) ~hg 60 kg4 nh æthf% [h c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc ahttc ì nh 6)4 ½ 60‛8 °K‛6) vxfi {htæ f æthf nh{{h ctlaçklc f 4=0 °K3 Th{cixíëc?

F 7 F0 *6 "δ Ξκ, F 7 F0 *6 " 4ζ Ξκ, F 7 60 R6 " 4 ½ 6)4 ½ 60‛8 ½ *4=0 ‛ 40,W F 7 60)01 kg4 Th{pc{~f? 60)01 kg4 >;

Xgf h{~f~xh~f nh cxtc acl fvxhklnf nh 48 °K f =8 °K) cd{htqfenc' '{h xg fxghe~c nh 4)6 kg; hg {hx qcixgh% [henc 6> ½ 60 ‛1 °K‛6 c kchalklhe' ~h nh nlif~fíëc ilehft nc cxtc) vxfi htf c qcixgh lelklfi nh{{f h{~f~xh~f3 Th{cixíëc?

ΞQ 7 Q0 λ λ Ξκ Ξκ ΞQ 7 Q0 ;ζ Ξκ

4)6 7 Q0 ½ ; ½ 6> ½ 60‛1 ½ *=8 ‛ 48, Q0 76)0 ½ 60; kg; Th{pc{~f? 6)0 ½ 60; kg;

>1

64<

*AMQ'[P, [xpcejf vxh qckï hekce~tf{{h eh{~f ptcqf c {hmxle~h

~h{~h? Kcg thifíëc fc aheþghec nf nlif~fíëc ~ìtglkf ec{ {ûilnc{) ì kctth~c fa ltgft ltgft vxh? *f, ~cnf nlif~fíëc) hg qhtnfnh) ckctth ef{ ~tï{ nlghe{øh{? iftmxtf) kcgptlghe~c h fi~xtf% *d, vxfenc xg kctpc vxh kce~ìg xg ctlaçklc nlif~f) f{ nlghe{øh{ nc ctlaçklc nlif~fg ~fgdìg% *k, c{ kcha lklhe~h{ lklhe~h{ nh nlif~fíëc ilehft) {xphtalklfi h qcixgì~tlkf) hg kctpc{ jcgcmïehc{ h l{û~tcpc{) mxftnfg) eh{~f ctnhg) f ptcpct' íëc nh 6 pftf 4 pftf ;% *n, f qftlfíëc nf{ nlghe{øh{ nh xg kctpc nhphenh nh {xf{ nlghe{øh{ nlghe{øh{ lelklfl{) nc kcha lklhe~h lklhe~h nh nlif~fíëc h nf qftlfíëc nh ~hgphtf~xtf {catlnf% *h, kcha lklhe~h{ lklhe~h{ nh nlif~fíëc {ëc mtfenhf{ fnlghe{lcefl{ h nhphe' nhg nc ~lpc nh gf~htlfi vxh kce{~l~xl c kctpc% Ef~xtfighe~h) f vxh{~ëc nhqhtlf {ht fexifnf) pct fpth{he~ft) fc ~cnc) f, ehejxgf fi~htef~lqf kctth~f% d, nxf{ fi~htef~lqf{ kctth~f{% k, ~tï{ fi~htef~lqf{ kctth~f{% n, vxf~tc fi~htef~lqf{ kctth~f{% h, ~cnf{ f{ fi~htef~lqf{ kctth~f{%

>>

Xgf pfehif nh fixgçelc pc{{xl) f 0 °K) xgf kfpfklnfnh nh 6 000 kg; *6 I,% [h ihqftgc{ f pfehif kcg æmxf fc acmc) f~ì vxh ckcttf hdxilíëc nf æmxf) {cd pth{{ëc ectgfi) vxfi {htæ f ecqf kfpfklnfnh nf pfehif3 Nfnc{? kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc fixgçelc 7 4> ½ 60 ‛1 °K‛62 kcha lklhe~h lklhe~h nh nlif~fíëc kÿdlkf nf æmxf 7 6); ½ 60 ‛> °K‛6% Th{cixíëc?

Pftf f pfehif? Q 7 Q0 *6 " ;ζ Ξκ, Q 7 6000 6 000 ½ R6 " ; ½ 4> ½ 60‛1 ½ *600 ‛ 0,W *kg;, Q 7 6000 6 000 " =)4 *kg;, Q 7 600=)4 6 00=)4 *kg;, Th{pc{~f? 6 00=)4 *kg;,

Th{cixíëc? f, Kctth~f%

F nlif~fíëc ~ìtglkf nh xg {ûilnc ckctth ef{ ~tï{ nlghe{øh{? kcg' ptlghe~c) iftmxtf h fi~xtf% d, Kctth~f% F nlif~fíëc nh xg {ûilnc ckctth {hgpth ’pftf actf‗% Jfqhenc xg ctlaç ' klc eh{{h {ûilnc) c ctlaçklc ~htæ {xf{ nlghe{øh{ fxghe~fnf{% k, Kctth~f% Hg {ûilnc{ jcgcmïehc{ h l{c~tûplkc{) c{ kcha lklhe~h{ lklhe~h{ nh nlif~f' íëc ilehft * ,) {xphta lklfi lklfi * , h qcixgì~tlkf * , mxftnfg f ptcpct' íëc? ζ 7 δ 7 λ

6

>8

C kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc fixgçelc ì 4)4 ½ 60 ‛8 °K‛6% Xg kxdc nh fixgçelc kcg qcixgh nh 8 I ì fvxhklnc nh >0 °A f~ì =1 °A%

4

;

n, Kctth~f% F qftlfíëc nh kfnf nlghe{ëc ilehft {catlnf pct xg kctpc {ûilnc)











6;0


>=

Xgf kjfpf nh fixgçelc pc{{xl xg axtc hg {xf pft~h khe~tfi% [henc fvxhklnf) cd{htqfgc{ vxh? f, ~fe~c f kjfpf kcgc c axtc ~henhg f nlglexlt {xf{ nlghe{øh{2 nlghe{øh{2 d, c axtc phtgfehkh kcg {xf{ nlghe{øh{ ctlmlefl{ h f kjfpf fx' ghe~f2 k, f kjfpf h c axtc phtgfehkhg kcg {xf{ nlghe{øh{ ctlmlefl{2 n, f kjfpf fxghe~f h c axtc nlglexl2 h, ~fe~c f kjfpf kcgc c axtc ~henhg f fxghe~ft {xf{ nlghe{øh{% Th{cixíëc?

Ec fvxhklghe~c) ~fe~c f kjfpf kcgc c ctlaçklc ~henhg f fxghe~ft {xf{ nlghe{øh{% C axtc kcgpct~f'{h kcgc {h h{~lqh{{h pthhekjlnc kcg c gf~htlfi nf kjfpf% Th{pc{~f? h >:

*XAGM, C kcha lklhe~h lklhe~h nh nlif~fíëc ~ìtglkf nc fixgçelc *F , ì) fptczlgfnfghe~h) nxf{ qhh{ c kchalklhe~h nh nlif~fíëc ~ìtglkf nc ahttc *Ah,% F almxtf gc{~tf nxf{ phíf{ hg vxh xg fehi ahl~c nh xg nh{' {h{ gh~fl{ heqciqh xg nl{kc ahl~c nc cx~tc% À ~hgphtf~xtf fgdlhe~h) c{ nl{kc{ h{~ëc pth{c{ fc{ feìl{%

Ah

F

F

Ah

[h f{ nxf{ phíf{ acthg fvxhklnf{ xelactghghe~h) ì kctth~c faltgft vxh? f, fphef{ c nl{kc nh F {h {ci~ftæ nc fehi nh Ah% d, fphef{ c nl{kc nh Ah {h {ci~ftæ nc fehi nh F% k, c{ ncl{ nl{kc{ nl{kc{ {h {ci~ftëc nc{ th{phk~lqc{ feìl{% n, c{ nl{kc{ eëc eëc {h {ci~ftëc nc{ feìl{% Th{cixíëc?

[henc ζF 5 ζAh) c fixgçelc nlif~ftæ gfl{ vxh c ahttc% F{{lg) fphef{ c fehi nh fixgçelc {h {ci~ftæ nf pifkf nh ahttc% Th{pc{~f? d

80

Xg nl{kc nh if~ëc nh 80)0 kg 4 nh æthf ì phtaxtfnc) a lkfenc lkfenc kcg xg axtc kltkxift nh 60)0 kg4 ef pc{líëc lenlkfnf ef almxtf% C kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc if~ëc ì nh 4 ½ 60‛8 °K‛6 h h{{f{ æthf{ {h thahthg à ~hgphtf' ~xtf fgdlhe~h% [h c nl{kc act kcickfnc hg xg actec h f ~hgphtf~xtf hihqfnf nh 600 °K) f æthf nc axtc? f, nlglexltæ nh 0)64 kg42 n, fxghe~ftæ nh 0)0> kg42 d, fxghe~ftæ nh 0)04 kg42 h, eëc {cathtæ fi~htfíëc% k, nlglexltæ nh 0)61 kg42 Th{cixíëc?

C axtc kcgpct~f'{h kcgc {h h{~lqh{{h pthhekjlnc kcg c gf~htlfi nf pifkf% ΞF 7 F0 4ζ Ξκ ΞF 7 60)0 ½ 4 ½ 4 ½ 60‛8 ½ 600 *kg4, ⇔ Th{pc{~f? n 86

Xgf pifkf gh~æilkf nh nlghe{øh{ 60 kg  40 kg  0)8 kg ~hg hg {hx khe~tc xg axtc kxoc nlägh~tc ì lmxfi f 6)00 kg vxfenc f pifkf h{~æ à ~hgphtf~xtf nh 40 °K% C kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc gh~fi nf pifkf ì 40 ½ 60 ‛1 °K‛6% Vxfenc f ~hgphtf~xtf ì nh 840 °K) f æthf nc axtc? f, fxghe~f 6(2 k, fxghe~f 4(2 h, eëc {h fi~htf% d, nlglexl 6(2 n, nlglexl 4(2 Th{cixíëc?

ΞF 7 F0 δ Ξκ ΞF 7 π T4 4ζ Ξκ

Pct~fe~c? F0 7 π T4 ↔ 600( ΞF 7 π T4 4ζ Ξκ ↔ z( 4 z 7 π T 4ζ Ξκ4 ½ 600 7 4 ½ 40 ½ 60‛1 *840 ‛ 40, 600 πT z 7 4( Th{pc{~f? k 84

><

*PXK'[P, Xg ghkäelkc nh fx~cgûqhl{ pthkl{f {ci~ft xg fehi

ΞF 7 0)0> kg4

H%T %T%%

Fc fvxhkhtgc{ xg {ûilnc nh 40 °K f :0 °K) cd{htqfgc{ vxh {hx qcixgh hzphtlghe~f xg fxghe~c kctth{pcenhe~h f 0)0<(












8;

Xgf dfttf nh h{~fejc ~hg f actgf nh xg ptl{gf th~c nh 4 >)0 kg nh æthf nf df{h h 6)0 g nh kcgptlghe~c) vxfenc ef ~hgphtf' ~xtf lelklfi nh 1: °A% [fdhenc vxh c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc ‛8 ‛6 h{~fejc ì lmxfi f 4)0 ½ 60 °K ) nh~htgleh c kcgptlghe~c h c qcixgh nh{{f dfttf vxfenc hif f~lemh f ~hgphtf~xtf nh 86: °A% Th{cixíëc?

600

7

ΞκA

6:0

6)4 Q0 7 Q0 ;ζ*660 ‛ ;0, 600 ζ 7 8)0 ½ 60‛8 °K‛6 Th{pc{~f? 8)0 ½ 60‛8 °K‛6 81

ΞκA 7 *86: ‛ 1:, °A 7 >80 °A ΞκK

⇔

κK

600

7 >80 6:0 ⇔ ΞκK 7 480 °K

Nlif~fíëc ilehft?

ΞI 7 I0 ζ Ξκ ΞI 7 6)0 ½ 4)0 ½ 60‛8 ½ 480

Xgf phíf {ûilnf ~hg xgf kfqlnfnh kxoc qcixgh qfih : kg ; f 40 °K% F ~hgphtf~xtf nf phíf qftlf pftf 840 °K h c kcha lklhe~h kcha lklhe~h nh nlif' ~fíëc ilehft nc {ûilnc *64 ½ 60 ‛1 °K‛6, pcnh {ht kce{lnhtfnc kce{~fe~h% [xpcenc vxh f pth{{ëc le~htef nf kfqlnfnh {hof {hgpth lmxfi à hz~ht' ef) vxfi f qftlfíëc phtkhe~xfi nc qcixgh nf kfqlnfnh3 Th{cixíëc?

ΞQ 7 Q0 λΞκ ΞQ 7 Q0 ;ζ Ξκ ΞQ 7 : ½ ; ½ 64 ½ 60‛1 *840 ‛ 40, ΞQ 7 0)6>> kg;

Pct~fe~c? ΞI 7 0)008 g I 7 I0 " ΞI 7 6)0 " 0)008 I 7 6)008 g

Pct~fe~c? Q0 7 : kg; ↔ 600( ΞQ 7 0)6>> kg; ↔ z(

Nlif~fíëc qcixgì~tlkf?

ΞQ 7 Q0 λ Ξκ ΞQ 7 FI ; ζ Ξκ ΞQ 7 >)0 ½ 600 ½ ; ½ 4)0 ½60‛8 ½ 480 ΞQ 7 1 kg ;

z 7 0)6>> ½ 600 ⇔ z 7 6):( : Th{pc{~f? 6):(

Pct~fe~c? Q 7 >01 kg;

Q 7 Q0 " ΞQ 7 >)0 ½ 600 " 1 ⇔ Th{pc{~f{? 6)008 g2 >01 kg

;

8=

*XGK'[P, F a lmxtf lmxtf gc{~tf f qftlfíëc thif~lqf nc kcgptlghe~c nh xgf dfttf gh~æilkf hg axeíëc nf ~hgphtf~xtf% Ξ

8>

Xg kxdc ì fvxhklnc h kce{~f~f'{h xg fxghe~c nh 0)1( ec {hx qcixgh% Vxfi acl f qftlfíëc nh ~hgphtf~xtf {catlnf phic kxdc3 Nfnc? kcha lklhe~h lklhe~h nh nlif~fíëc qcixgì~tlkf nc gf~htlfi nc kxdc 7 1)0 ½ 60‛1 °K‛6 Q0 ↔ 600( ΞQ ↔ 0)1( ⇔ ΞQ 7



*gg#g, 4)>

0

Th{cixíëc?

Kcgc ΞQ 7 Q0 λ λ Ξκ Ξκ he~ëc

6;6

0)1 Q0 600

600 60 0

κ *°K,

[h xg kxdc nh fth{~f f) ahl~c nh{{h gh~fi) act {xdgh~lnc à qftlfíëc nh ~hgphtf~xtf nh 600 °K) {xf nlif~fíëc qcixgì~tlkf {htæ? f, ΞQ 7 =)4 ½ 60‛; f;% n, ΞQ 7 >): ½ 60‛; f;% d, ΞQ 7 1)0 ½ 60‛; f;% h, ΞQ 7 ;)1 ½ 60‛; f;% ‛; ; k, ΞQ 7 8)1 ½ 60 f %













6;4


8:

*Gfkb'[P, Xgf h{ahtf nh kht~f ilmf gh~æilkf) fc {ht fvxhklnf nh 600 °K) ~hg {hx qcixgh fxghe~fnc nh >)8(% Xgf jf{~h nh{{f gh{gf ilmf gh~æilkf) fc {ht fvxhklnf nh 600 °K) ~htæ {hx kcgptlghe~c fxghe' ~fnc nh? f, 6)0(% k, 4)0(% h, >)8(% d, 6)8(% n, ;)0(%

16

C ncec nh xg pc{~c nh mf{cilef kce{xi~f xgf ~fdhif nh kchalklhe' ~h{ nh nlif~fíëc qcixgì~tlkf) qcixgì~tlkf) cd~henc pftf c æikcci æikcci c qfict 6 ½ 60 ‛; °K‛6% F{{lg) hih qhtla lkf lkf vxh {h kcgptft 40 000 I nh æikcci hg xg nlf hg vxh f ~hgphtf~xtf ì nh 4= °K h qhenï'ic{ hg xg nlf atlc f 68 °K) h{~ftæ ~henc xg pthoxçc nh e il~tc{% Vxfi c qfict nh e3 Th{cixíëc?

Th{cixíëc?

Ef nlif~fíëc qcixgì~tlkf? Q0 ↔ 600( ΞQ ↔ >)8( Q >)8 ΞQ 7 0 600 Kcgc? ΞQ 7 Q0 ;ζ Ξκ he~ëc? Q0 >)8 ζ Ξκ 600 7 Q0 ; ζ Ξκ 7 0)068 Ef nlif~fíëc ilehft? ΞI 7 I0 ζ Ξκ ΞI 7 ζ Ξκ I0 h? I0 ↔ 600 ( ΞI ↔ z( z 7 ΞII600 0 F{{lg? z 7 ζ Ξκ 600 ⇔ z 7 0)068 ½ 600 ⇔ z 7 6)8(

ΞQ 7 Q0 λ λ Ξκ Ξκ

e 7 40000 40 000 ½ 6 ½ 60‛; ½ *68 ‛ 4=, *, e 7 ‛ 4>0  C {lefi ehmf~lqc lenlkf vxh jcxqh xgf nlglexlíëc ec qcixgh nc æikcci% F{{lg? e 7 4>0  Th{pc{~f? 4>0 14

H%T %T%%

Xg atf{kc nh qlntc) mtfnxfnc hg kg ; f 0 °K) kce~ìg ght' kÿtlc f~ì f gftkf nh 600)0 kg ;) vxfenc flenf f 0 °K% Fc {h fvxhkht c kceoxe~c f 640 °K) c eçqhi nh ghtkÿtlc f~lemh f gftkf nh 606): kg ;% Nh~htgleh c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc qlntc% Nfnc? kchalklhe~h nh nlif~fíëc nc ghtkÿtlc? λ Jm 7 6: ½ 60‛8 °K‛6 Th{cixíëc?

F nlahtheíf nh ihl~xtf kctth{pcenh à nlif~fíëc fpfthe~h nc içvxl' nc) pcl{ eëc pcnhgc{ ec{ h{vxhkht nh vxh c atf{kc ~fgdìg {h nlif~cx? ΞQfpfthe~h 7 606): ‛ 600)0 ΞQfpfthe~h 7 6): kg;

X{fgc{ f hzpth{{ëc nf nlif~fíëc fpfthe~h nc{ içvxlnc{?












1>

Hg xg thklplhe~h nh pctkhifef) mtfnxfnc kctth~fghe~h hg khe~çgh~tc{ kÿdlkc{ f ;0 °K) ì kcickfnc ph~tûihc f ;0 °K f~ì f gftkf 800 kg;% Hg {hmxlnf) hihqf'{h f ~hgphtf~xtf nc kceoxe~c f =0 °K% Nfnc{? kchalklhe~h nh nlif~fíëc kÿdlkf nc ph~tûihc 7 <)6 ½ 60 ‛> °K‛62 kchalklhe~h nh nlif~fíëc ilehft nf pctkhifef 7 ;); ½ 60 ‛1 °K‛6% Nh~htgleh? f, c kcha lklhe~h lklhe~h nh nlif~fíëc fpfthe~h nc ph~tûihc) vxfenc ghnlnc ec atf{kc nh pctkhifef2 d, f gftkf f~lemlnf phic phic ph~tûihc ec atf{kc) atf{kc) fpû{ c fvxhklghe~c2 fvxhklghe~c2 k, f nlif~fíëc thfi {catlnf phic ph~tûihc% Th{cixíëc?

f, λ fp 7 λ t ‛ λ a λ fp 7 λ t ‛ ;ζa λ fp 7 *<)6 ½ 60‛> ‛ ; ½ ;); ½ 60‛1, *°K‛6, λ fp 7 <)0 ½ 60‛> °K‛6

d, ΞQfp 7 Q0 λ fp Ξκ ΞQfp 7 800 ½ <)0 ½ 60‛> ½ *=0 ‛ ;0, ΞQfp 7 6: kg; Pct~fe~c? Qfp 7 Q0 " ΞQfp 7 800 " 6: Qfp 7 86: kg; k, ΞQt 7 Q0 λ t Ξκ ΞQt 7 800 ½ <)6 ½ 60‛> ½ *=0 ‛ ;0, ΞQt 7 6:)4 kg; Th{pc{~f{? f, <)0 ½ 60‛> °K‛62 d, 86: kg;2 k, 6:)4 kg; 18

*Xel{f'[P, Xg thklplhe~h nh qlntc nh 680 kg ; h{~æ kcgpih~f'

1=

6;;

Ncl{ thklplhe~h{ nh 6 000 kg; kfnf xg) f 0 °K) actfg x{fnc{ ef nh~htglefíëc nc kcha lklhe~h lklhe~h nh nlif~fíëc fpfthe~h nc ghtkÿtlc% Xg nc{ thklplhe~h{ htf nh kcdth h c cx~tc) nh fixgçelc% Fpû{ {hthg ~c~fi' ghe~h kjhlc{ nh ghtkÿtlc) ~fgdìg f 0 °K) c{ kceoxe~c{ actfg fvxhkl' nc{ f~ì 600 °K% Nh~htgleh? f, c{ kchalklhe~h{ nh nlif~fíëc fpfthe~h hekce~tfnc{ pftf c ghtkÿtlc2 d, c qcixgh nh ghtkÿtlc hz~tfqf{fnc hg kfnf kf{c% lklhe~h nh nlif~fíëc kÿdlkf nc ghtkÿtlc 7 6): ½ 60 ‛> °K‛62 Nfnc{? kcha lklhe~h kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc kcdth 7 6)1 ½ 60 ‛8 °K‛62 kcha lklhe~h lklhe~h nh nlif~fíëc ilehft nc fixgçelc 7 4)> ½ 60 ‛8 °K‛6% Th{cixíëc?

f, λ fp 7 λ t ‛ λ a λ fp *ec kcdth, 7 6): ½ 60‛> ‛ ; ½ 6)1 ½ 60‛8 λ fp *ec kcdth, 7 6);4 ½ 60‛> °K‛6 λ fp *ec fixgçelc, 7 6): ½ 60‛> ‛ ; ½ 4)> ½ 60‛8 λ fp *ec fixgçelc, 7 6)0: ½ 60‛> °K‛6

d, ΞQfp 7 Q0 λ fp Ξκ 6 000 ½ 6);4 ½ 60‛> *600 ‛ 0, ΞQfp *ec kcdth, 7 6000 ΞQfp *ec kcdth, 7 6;)4 kg;

6 000 ½ 6)0: ½ 60‛> *600 ‛ 0, ΞQfp *ec fixgçelc, 7 6000 ΞQfp *ec fixgçelc, 7 60): kg; Th{pc{~f{? f, 6)0: ½ 60‛> °K‛62 d, 60): kg;











6;>


1<

*Axqh{~'[P, Xg ~htgþgh~tc h{phklfi) kcg içvxlnc nhe~tc nh xg thklplhe~h nh qlntc) ì kce{~l~xçnc nh xg dxidc nh 6 kg ; h xg ~xdc kcg {hkíëc ~tfe{qht{fi nh 6 gg 4% À ~hgphtf~xtf nh 40 °K) c içvxlnc pth' hekjh kcgpih~fghe~h c dxidc f~ì f df{h nc ~xdc% À ~hgphtf~xtf nh 80 °K) c içvxlnc pthhekjh c ~xdc f~ì xgf fi~xtf nh 64 gg% Kce{lnhth nh{pthçqhl{ c{ hahl~c{ nf nlif~fíëc nc qlntc h nf pth{{ëc nc mæ{ fklgf nf kcixef nc iç' vxlnc% Pcnhgc{ faltgft vxh c kchalklhe~h nh nlif~fíëc qcixgì~tlkf gìnlc nc içvxlnc qfih? f, ; ½ 60‛> °K‛6% d, > ½ 60‛> °K‛6% 64 gg ‛> ‛6 k, 64 ½ 60 °K % n, 40 ½ 60‛> °K‛6% h, ;1 ½ 60‛> °K‛6% Dxidc

=4

Xg thklplhe~h nh 400 kg; nh kfpfklnfnh) ahl~c nh xg gf~h' tlfi nh kcha lklhe~h lklhe~h nh nlif~fíëc qcixgì~tlkf nh 600 ½ 60‛1 °K‛6) kce~ìg 6:0 kg; nh xg içvxlnc nh kcha lklhe~h lklhe~h nh nlif~fíëc kÿdlkf nh 6 000 ½ 60‛1 °K‛6% F ~hgphtf~xtf nc {l{~hgf ì nh 40 °K% Vxfi f ~hgph' tf~xtf'ilgl~h nh fvxhklghe~c nc içvxlnc {hg vxh jfof ~tfe{dctnf' ghe~c3 Th{cixíëc?

ΞQfp 7 Q0 λ fp Ξκ

*400 ‛ 6:0, 7 6:0 *6 *6000 000 ½ 60‛1 ‛ 600 ½ 60‛1, *κ6 ‛ 40, 40 7 6:0 ½ < ½ 60‛> *κ6 ‛ 40, 64; 7 κ6 ‛ 40 κ6



6>; °K

Th{cixíëc?

Th{pc{~f?

ΞQ 7 Q0 λ λ Ξκ Ξκ F j 7 Q 0 λ λ Ξκ Ξκ

=;



6>; °K

Th{pc{~f? d

*XAPH, Xg thklplhe~h gh~æilkc nh 60 il~tc{ h{~æ kcgpih~fghe~h kjhlc nh ûihc) vxfenc f ~hgphtf~xtf nc kceoxe~c ì nh 40 °K% Hihqfe' nc'{h f ~hgphtf~xtf f~ì ;0 °K) xg qcixgh lmxfi f :0 kg ; nh ûihc ~tfe{' dctnf% [fdhenc'{h vxh c kchalklhe~h nh nlif~fíëc qcixgì~tlkf nc ûihc ì lmxfi f 0)< ½ 60 ‛; °K‛6) vxfi acl f nlif~fíëc nc thklplhe~h hg kg ;3

=0

Th{cixíëc?

6 ½ 64 7 6000 ½ λ *80‛40, λ 7 > ½ 60‛> °K‛6

Xg kcghtklfe~h kcgptcx 60 000 I nh æikcci exg nlf hg vxh f ~hgphtf~xtf htf nh 64 °K% Pftf cd~ht xg ixktc hz~tf nh 4() th{ciqhx h{phtft xg nlf hg vxh f ~hgphtf~xtf ac{{h ) pftf c hemfttfafghe' ~c% [fdhenc vxh c kcha lklhe~h kcha lklhe~h nh nlif~fíëc qcixgì~tlkf nc æikcci ì nh ‛; ‛6 6 ½ 60 °K ) nh~htgleh h{{f ~hgphtf~xtf % Th{cixíëc?

Q0 ↔ 600( ΞQ ↔ 4(

Kæikxic nf nlif~fíëc nc ûihc? ΞQ 7 Q0 λ Ξκ ΞQûihc 7 60> ½ 0)< ½ 60‛; *;0 ‛ 40, *kg;, ΞQ 7 <0 kg; F nlif~fíëc nc thklplhe~h ì f nlahtheíf he~th f nlif~fíëc nc ûihc h c ûihc ~tfe{dctnfnc% F{{lg? ΞQ

7 *<0 ‛ :0 , *kg;, ⇔

ΞQ

7 60 kg;












=8

*XAMC'MC, Exg nlf vxhe~h hg Mcläelf) ;4 °K) xgf ncef'nh'kf{f kcickf æikcci hg xg thklplhe~h nh qlntc mtfnxfnc h ifktf'c dhg pftf hql' ~ft hqfpctfíëc% Nh gfntxmfnf) kcg c ~htgþgh~tc fkx{fenc 64 °K) hif ec~f) {xtpth{f) vxh) fph{ft nh c qlntc h{~ft dhg ahkjfnc) c qcixgh nh æikcci thnxlx'{h% [fdh'{h vxh c {hx h{pfe~c eëc {h ox{~lalkf) pcl{ {h ~tf~f nc aheþghec nf nlif~fíëc ~ìtglkf% F nlglexlíëc nc qcixgh acl nh? f, 6)6(% k, ;);(% h, 1)1(% d, 4)4(% n, >)>(% Kce{lnhth c kcha lklhe~h lklhe~h nh nlif~fíëc ~ìtglkf qcixgì~tlkf nc æikcci? λ æikcci 7 6)6 ½ 60‛; °K‛6 55 λ qlntc Th{cixíëc?

Kce{lnhtfenc nh{pthçqhi f nlif~fíëc nc qlntc) ~hgc{? ΞQ 7 Q0 λ Ξκ ΞQ 7 Q; 6)6 ½ 60‛; *64 ‛ ;4, ΞQ 7 ‛44 ½ 60‛; Q0 Kcgc? Q0 ↔ 600( ΞQ ↔ z( z 7 ΞQ 600 Q0 he~ëc? *‛44 ½ 60‛; Q0, 600 z 7 ‛4)4( ⇔ z7 Q0 C {lefi ehmf~lqc lenlkf vxh jcxqh xgf nlglexlíëc nh 4)4( ec qcixgh nc æikcci% Th{pc{~f? d

6;8

8 ½ 60‛> *κa ‛ 40, 7 0)08 κa ‛ 40 7

0)08 ½ 60> ⇔ κa ‛ 40 7 600 ⇔ 8

κa 7 640 °K

Th{pc{~f? 640 °K =:

Xgf {xd{~äeklf ~hg gf{{f h{phkçalkf nh 0)=: m#kg ; f 48 °K h 0)18 m#kg; f >48 °K% Vxfi c {hx kchalklhe~h nh nlif~fíëc qcixgì~tlkf3 Th{cixíëc?

¸0 ¸ 7 *6 " λΞκ , ¸ 6 " λ Ξκ 7 ¸0 ⇔ 6 " λ *>48 *>48 ‛ 48, 7 0)=: 0)18 >00λ 7 6)4 ‛ 6 >00λ 7 0)4 ⇔ λ 7 8 ½ 60 ‛> °K‛6 Th{pc{~f? 8 ½ 60‛> °K‛6 =<

*PXK'[P, F æmxf fpth{he~f xgf fecgfilf hg thifíëc fc{ nh' gfl{ içvxlnc{% F{{lg) f ~hgphtf~xtf nh > °K ì? f, fvxhif pftf f vxfi f æmxf ~hg gflct nhe{lnfnh% d, fvxhif pftf f vxfi f æmxf f{{xgh gflct qcixgh% k, f gfl{ dflzf dflzf vxh f æmxf f~lemh ec h{~fnc içvxlnc% n, f kctth{pcenhe~h fc pce~c ~tlpic nf æmxf% h, f nh ax{ëc nc mhic% Th{cixíëc?

n7 g











6;1


:6

*Gfkb'[P, Nl xg nl~fnc pcpxift? ’F ef~xthf ì {ædlf&‗% Nh af~c& Fc cd{htqftgc{ c{ nlqht{c{ aheþghec{ nf ef~xthf) a lkfgc{ a lkfgc{ hekfe' ~fnc{ kcg gxl~c{ pctghecth{) {hg c{ vxfl{ eëc pcnhtçfgc{ ~ht qlnf ef afkh nf ^httf) kceactgh f kcejhkhgc{% Xg nh{{h{ pctghecth{) nh hz~thgf lgpct~äeklf) ì c kcgpct~fghe~c feþgfic nf æmxf) ec h{' ~fnc içvxlnc) nxtfe~h {hx fvxhklghe~c cx th{atlfghe~c {cd pth{{ëc ectgfi% [h eëc hzl{~l{{h ~fi kcgpct~fghe~c) f qlnf {xdfvxæ~lkf ec{ ifmc{ h tlc{) ptleklpfighe~h nf{ thmløh{ gfl{ atlf{ nh ec{{c pifeh~f) eëc {htlf pc{{çqhi% Nc{ mtæa lkc{ lkc{ fdflzc) c vxh ghijct thpth{he~f h{{h kcgpct~fghe~c feþgfic ì? f, n, , ;

, ;

g k * h g x i c Q

g k * h g x i c Q

0 >

^hgphtf~xtf *°K,

d,

0 6>)8

0

k,

^hgphtf~xtf *°K,

, ;

g k * h g x i c Q

g k * h g x i c Q

>

^hgphtf~xtf *°K,

, ;

g k * h g x i c Q

0 6>)8 68)8 ^hgphtf~xtf *°K,

Th{cixíëc?

C qcixgh nh kht~f gf{{f nh æmxf ì

0

*Gfkb'[P, ^tï{ dfttf{ gh~æilkf{) F) D h K) ~ïg) f 0 °K) {hx{ kcg' > 4 ptlghe~c{ ef ptcpctíëc 0F 7 0D 7 0K % Pftf vxh h{{f ptcpctíëc 8 ; {h gfe~hejf kce{~fe~h f vxfivxht ~hgphtf~xtf *hevxfe~c eëc jcx' qht gxnfeíf nh h{~fnc nh fmthmfíëc gcihkxift,) c{ kchalklhe~h{ nh nlif~fíëc ilehft nc{ gf~htlfl{ nf{ th{phk~lqf{ dfttf{ nhqhtëc h{~ft ef ptcpctíëc? f, ζF 7 ζD 7 ζK% n, ζF 7 8 7 ; % >ζD 4ζK >ζ 4ζ d, ζF 7 D 7 K % h, ζF 7 > 7 4 % 8 ; 8ζD ;ζK 8ζ ;ζ k, ζF 7 D 7 K % > 4 Th{cixíëc?

h,

, ;

:;

6>)8

^hgphtf~xtf *°K,

[h f ptcpctíëc lenlkfnf qfih pftf vxfivxht ~hgphtf~xtf) ~hgc{? >D 4K F 7 8 7 ; X{fenc?  7 0*6 " ζ Ξκ, qhg? >0 *6 " ζD Ξκ, 40 *6 " ζK Ξκ, D K 7 ) 0 *6 " ζF Ξκ, 7 8 ; F gf{ >0 40 D 7 K 0 7 8 ; F F{{lg) {lgpila lkfenc) lkfenc) ~hgc{? 6 " ζF Ξκ 7 6 " ζD Ξκ 7 6" ζK Ξκ Nh cenh kcekixçgc{ vxh? ζF 7 ζD 7 ζK














:8

*PXK'[P, Xgf dfttf nh fixgçelc) lelklfighe~h f 40 °K) ~hg) f h{{f ~hgphtf~xtf) xgf nhe{lnfnh ilehft nh gf{{f lmxfi f 4): ½ 60‛; m#gg% F dfttf ì fvxhklnf {cathenc xgf qftlfíëc nh kcgptlghe~c nh ; gg% [fdh'{h vxh c kcha lklhe~h lklhe~h nh nlif~fíëc ilehft ~ìtglkf nc fixgçelc ì ‛8 ‛6 4)> ½ 60 °K h {hx kfict h{phkça lkc lkc ì 0)4 kfi#m °K% F vxfe~lnfnh nh kfict fd{ctqlnf phif dfttf ì? f, ;8 kfi% n, 6>0 kfi% d, =0 kfi% h, 800 kfi% k, <0 kfi%

6;=

:=

Xgf dfttf nh kcdth acl thkxtqfnf ~cgfenc f actgf nh xgf {h' glkltkxeahtïeklf% F{ hz~thglnfnh{ actfg xelnf{ pct xgf cx~tf dfttf th~f kce{~l~xçnf pct ncl{ gh~fl{? xgf pft~h) nh kcgptlghe~c z) htf nh lekc h f cx~tf) nh kcgptlghe~c |) nh pif~lef% Kcdth

Th{cixíëc?

ΞI 7 I0 ζ Ξκ

; 7 I0 4)> 60‛8 Ξκ I0 Ξκ 7 6)48 ½ 608 Kcgc? V 7 g k Ξκ h? g 7 I0 n 7 I0 4): ½ 60‛;) qhg? V 7 I0 4): ½ 60‛; ½ 0)4 Ξκ ⇔ V 7 0)81 ½ 60‛; *I0 Ξκ, V 7 0)81 ½ 60‛; ½ 6)48 ½ 608 ⇔

V 7 =0 kfi

_lekc

Pif~lef

z

|

[ëc nfnc{ c{ kchalklhe~h{ nh nlif~fíëc ilehfth{? kcdth 7 6= ½ 60 ‛1 °K‛62 lekc 7 4< ½ 60 ‛1 °K‛62 pif~lef 7 < ½ 60 ‛1 °K‛6% Pftf vxh c ftkc nh kcdth kce{htqh {xf actgf {hglkltkxift) f vxfivxht ~hgphtf~xtf f vxh {hof ihqfnc) f tfëc z he~th c{ kcgptlghe~c{ | lelklfl{ z h nc{ {hmghe~c{ nh lekc h pif~lef nhqh {ht?











6;:


Kcgc?

Th{cixíëc?

I 4π 0 7 ^0) m

Pftf c{ ifnc{ FD h DK? ΞI 7 I0 ζ Ξκ ΞIFD 7 ΞIDK 7 4 ζ Ξκ Pftf c ifnc FK? ΞI 7 I0 ζ Ξκ ΞIFK 7  4 ζ Ξκ F{{lg?

qhg? ^ 7 ^0 6 " ζΞκ Pct~fe~c? ^ 7 ^0 6 " 6 ½ 60‛8 R‛>0 ‛*40,W ^ 7 ^0 6 ‛ 1 ½ 60‛> 7 ^0 6 ‛ 0)0001 ^ 7 0)<<<1< ^0 F{{lg) hg xg nlf *:1 >00 {, c thiûmlc ltæ fnlfe~ft) gftkfenc? 6 nlf 7 *:1>00 *:1 >00 ½ 0)<<<1<, { 7 :1;=;)44 :1 ;=;)44 { F nlahtheíf kctth{pcenh f? *:1 >00 ‛ :1;=;)44, :1 ;=;)44, { ⇔ Ξ~ 7 *:1>00

Ξ~



41 {

Th{pc{~f? d :<

*XADF, F jf{~h nh xg pïenxic ì ahl~f kcg xg gf~htlfi) kxoc

ΞIFD 7 ΞIDK 7 ΞIFK Th{pc{~f? h <6

*Xelqh{~'[P, Xg ftfgh ì hekxtqfnc hg actgf nh xg ftc klt' kxift nh tflc T) ~henc) pctìg) xgf acimf n he~th {xf{ hz~thglnfnh{) kceactgh lenlkf f almxtf fdflzc% Fvxhkhenc'{h h{{h ftfgh) ì kctth~c fa ltgft ltgft vxh f ghnlnf nh T h f ghnlnf nh n) th{phk~lqfghe~h? f, fxghe~ftæ „ eëc {h fi~htftæ% d, fxghe~ftæ „ fxghe~ftæ% fxghe~ftæ% T k, fxghe~ftæ „ nlglexltæ% n n, eëc {h fi~htftæ „ fxghe~ftæ%












<;

*Qxeh{p'[P, Xgf tìmxf nh fíc nh kcha lklhe~h lklhe~h nh nlif~fíëc ilehft ‛8 ‛6 ζ 7 6)4 ½ 60 °K acl kfildtfnf f kht~f ~hgphtf~xtf) nh ~fi gcnc vxh c httc gæzlgc hg kfnf nlql{ëc nh gliçgh~tc ì nh 1)0 ½ 60 ‛8 gg% Vxfi ì c le~htqfic gæzlgc nh ~hgphtf~xtf{ hg vxh h{{f tìmxf pcnh {ht x{f' nf) hg ~ctec nf ~hgphtf~xtf nh kfildtfíëc) {h {h pth~henh kce{htqft fvxhif pthkl{ëc3

<1

*Xeh{p'[P, F almxtf gc{~tf xgf iäglef dlgh~æilkf) nh kcg' ptlghe~c I0 ef ~hgphtf~xtf ^0) vxh nhqh ~ckft c kce~f~c K vxfenc fvxhklnf% F iäglef ì ahl~f nc{ gh~fl{ L h LL) kxof{ qftlfíøh{ thif~lqf{ nc kcgptlghe~c ΞI hg axeíëc nf qftlfíëc nh ~hgphtf~xtf Ξ^ 7 ^ ‛ ^ 0 I0 hekce~tfg'{h ec mtæa lkc% lkc% Iäglef dlgh~æilkf) hg ^ 7 ^ 0

Th{cixíëc?

ΞI 7 I0 ζ Ξκ

1)0 ½ 60‛8 7 6)0 ½ 6)4 ½ 60‛8 ½ Ξκ

K

Ξκ 7 8)0 °K Th{pc{~f? 8)0 °K

ΞI

I0

*½ 60‛1, =00

<>

*Gfkb'[P, Kcg xgf tìmxf nh if~ëc *kchalklhe~h nh nlif~fíëc ilehft 4)0 ½ 60‛8 °K‛6, fahtlnf f 40 °K) ghnh'{h f nl{~äeklf he~th ncl{ pce~c{% H{{f ghnlnf acl hah~xfnf f xgf ~hgphtf~xtf fklgf nh 40 °K) gc~lqc phic vxfi fpth{he~f xg httc nh 0)08(% F ~hgphtf~xtf ef vxfi acl ahl~f h{{f ghnlnf ì? f, 80 °K% n, ;8 °K%

6;<

100

LL

800 >00 ;00

L











6>0


<=

*L^F'[P, Xg nl{kc nh hdcel~h ~hg xg ctlaçklc kltkxift nh nlägh' ~tc 6 kg) ickfilfnc hg {hx khe~tc% [fdhenc'{h vxh c kcha lklhe~h kcha lklhe~h nh ‛1 ‛6 nlif~fíëc {xphta lklfi lklfi nc hdcel~h ì lmxfi f 610 ½ 60 °K ) pcnh'{h fa lt' lt' gft vxh f æthf nc ctlaçklc) vxfenc f ~hgphtf~xtf nc nl{kc qftlf nh 60 °K pftf 600 °K) f, nlglexl nh ;1π ½ 60‛> kg4% n, nlglexl nh 6>>π ½ 60‛> kg4% d, fxghe~f nh 6>>π ½ 60‛> kg4% h, phtgfehkh lefi~htæqhi% k, fxghe~f nh ;1π ½ 60‛> kg4% Th{cixíëc?

ΞF 7 F0 δ Ξκ ΞF 7 T04 δ Ξκ ΞF 7 *0%8,4 ½ 610 ½ 60‛1 ½ *600 ‛ 60, *kg4, ΞF 7 ;1  ½ 60‛> kg4 Th{pc{~f? k <:

F almxtf vxh qckï cd{htqf eh{~f vxh{~ëc thpth{he~f xg hlzc vxh ~tfdfijf kcg acimf) heqci~c pct xg fehi ahl~c nc gh{gc gf~htlfi nc hlzc *kchalklhe~h nh nlif~fíëc ilehft lmxfi f ,% F xgf ~hgphtf~xtf fgdlhe~h nh 40 °K) f acimf he~th c hlzc h c fehi ì lmxfi f *n 7 T ‛ T ,%

600

*XADF, F a lmxtf lmxtf thpth' T {he~f xg dfiëc) nh qcixgh Q 0) ahl~c nh gf~htlfi l{û~tcpc nh kcha lklhe~h lklhe~h nh nlif~fíëc ilehft % C dfiëc h{~æ kcgpih~fghe' ~h kjhlc nh xg içvxlnc nh kch' a lklhe~h lklhe~h nh nlif~fíëc qcixgì~tl' kf h nh gf{{f h{phkçalkf ι0) à ~hgphtf~xtf κ0% Vxfenc f ~hg' phtf~xtf nc dfiëc ì fxghe~fnf hg Ξκ) hz~tfqf{f c qcixgh Q h nc içvxlnc% Eh{{f{ kcenlíøh{) pcnh'{h faltgft? *06, C tflc T nlglexl vxfenc f ~hgphtf~xtf nc dfiëc fxghe~f% *04, C dfiëc {h nlif~f kcgc {h ac{{h gfklíc% gfklíc% *0>, C kcha lklhe~h lklhe~h nh nlif~fíëc fpfthe~h nc içvxlnc ì hzpth{{c pct λ " ;ζ% *0:, Fpû{ f qftlfíëc nh ~hgphtf~xtf Ξκ) f gf{{f h{phkçalkf nc içvxlnc pf{{f f {ht hzpth{{f pct ι0*6 " λ Ξκ,‛6% *61, F nlif~fíëc nc dfiëc ì Q0 λ Ξκ ‛ Qh% Nï kcgc th{pc{~f f {cgf nc{ eÿghtc{ f{{cklfnc{ à{ faltgf~lqf{ kctth~f{%












604

F a lmxtf lmxtf {hmxle~h gc{~tf xg nl{pc{l~lqc x~lilfnc pftf ghnlt c kcha lklhe~h lklhe~h nh nlif~fíëc kÿdlkf nh xg içvxlnc% Xg nc{ tfgc{ qht~lkfl{ nc ~xdc hg actgf nh X) vxh kce~ìg c içvxlnc hg h{~xnc) ì h{atlfnc kcg mhic f 0 °K) hevxfe~c c cx~tc tfgc ì fvxhklnc x~lilfenc'{h qfpct nh æmxf f 600 °K% Ghtkÿtlc

n, pftf xgf qftlfíëc qftlfíëc nh 60 °K ef ~hgphtf~xtf nh 600 il~tc{ nh mf{cil' ef) jæ xg fxghe~c nh qcixgh lmxfi f 0)01; il~tc% h, c qcixgh hz~tfqf{fnc hz~tfqf{fnc nh xg ~fevxh ~fevxh nh mf{cilef ~c~fighe~h ~c~fighe~h kjhlc kcg 400 il~tc{ ì fptczlgfnfghe~h >)>: il~tc{ vxfenc jæ xg fx' ghe~c nh ~hgphtf~xtf nh 48 °K% Th{cixíëc? f, Lekctth~f

Qfpct

Mhic

6>6

Qfpct

H{{h nl{pc{l~lqc acl x{fnc pct Nxicem'Ph~l~ pftf f cd~heíëc nc kcha l'l'

F nlglexlíëc nc qcixgh nf mf{cilef ì gflct vxh f nc ~fevxh% d, Lekctth~f F mf{cilef ì kcgptfnf pct il~tc% F{{lg) hg ~hgphtf~xtf{ gflcth{ hekce~tfgc{ ghec{ mf{cilef hg xg il~tc% k, Lekctth~f λ fp 7 λ t ‛ λ a 7 <)1 ½ 60‛> ‛ 1; ½ 60‛1 λ fp 7 <)1 ½ 60‛> ‛ 0)1; ½ 60‛> ⇔ λ fp 7 :)<= ½ 60‛> °K‛6 n, Lekctth~f ΞQ 7 Q0 λ Ξκ ΞQ 7 600 ½ <)1 ½ 60‛> ½ 60 ⇔ ΞQ 7 0)<1  h, Kctth~f Ξfp 7 Q0 λ fp Ξκ ΞQfp 7 400 ½ :)<= ½ 60‛> ½ 48 ⇔

ΞQfp



>)>: 













6>4


Kcgc? n 7 g ⇔ g 7 n Q) he~ëc? Q *n Q k Ξκ,æmxf " *K Ξκ,gfgfnhltf 7 0 6 ½ 480 ½ 6 *<4 ‛ <:, " K *<4 ‛ ;4, 7 0 ‛6800 " 10K 7 0

601

*XAM'MC, Ox{~lalvxh) nh gcnc {xkle~c) f fa ltgfíëc? fa ltgfíëc? ’Xg kct' pc a ix~xf ix~xf hg æmxf f 40 °K% Vxfenc f ~hgphtf~xtf nf æmxf {xdlt pftf >0 °K) c qcixgh {xdght{c { xdght{c nc kctpc fxghe~ftæ‗% Th{pc{~f? F nhe{lnfnh nf æmxf nlglexl kcg c fxghe~c nh ~hgph'

tf~xtf) eh{{h le~htqfic% Nh{{f actgf) c kctpc alkf gfl{ nhe{c vxh f æmxf h c qcixgh {xdght{c fxghe~f%

10K 7 6 800 K 7 48 kfi#°K

60=

*Xelah{p'[P, C ~fevxh nh hzpfe{ëc ~ìtglkf ì xgf ~hkecicmlf












60:

*XA[Kft'[P, Fe~h{ nh lelklft c ~tfe{pct~h nh kcgdx{~çqhl{) c{ ncl{ ~fevxh{ lelklfighe~h qflc{ {h hekce~tfqfg à ~hgphtf~xtf nh 68 °K) dhg kcgc c{ içvxlnc{ vxh ehih{ {htlfg nhttfgfnc{% Ec ptlghltc ~fevxh) actfg nh{phofnc{ 68 000 I nh mf{cilef h) ec {h' mxenc) 40 000 I nh æikcci% Nxtfe~h c ~tfe{pct~h) f act~h le{cifíëc ah kcg vxh f ~hgphtf~xtf ec le~htlct nc{ ~fevxh{ kjhmf{{h f ;0 °K% Nfnc{? Mf{cilef ‛ kcha lklhe~h lklhe~h nh nlif~fíëc qcixgì~tlkf <)1 z 60 ‛> °K‛62

Æikcci ‛ Nhe{lnfnh 0): m#kg;2 Kfict h{phkçalkc 0)1 kfi#*m% °K,%

Th{cixíëc? Nlif~fíëc ilehft?

I0 ↔ 600( 4I ΞI ↔ 4( ⇔ ΞI 7 0 600 Kcgc? ΞI 7 I0 ζ Ξκ) ~hgc{? 4I0 7 I ζ Ξκ ⇔ ζ Ξκ 7 0)04 600 0

6>;











6>>


Fvxhkhenc'{h f dfttf) hif {h hzpfenh h af c plec kliçentlkc *nh 8)0 gg nh tflc, tcift hg ~ctec nc hlzc alzc) gcqhenc c pce~hltc% Dfttf

Hlzc alzc à pif~factgf

F{{lg? ^ 7 m“ 7 m ^“

MGg *T " j,4 MGg T4

^7 T ^“ *T " j, 4, Fi~htfenc'{h f ~hgphtf~xtf) fc pì nf ~ctth? ~ctth? ^ 7 4π I0 m












Kcgc? z4 7 f4 " d4 h f 7 4d) ~hgc{? *f4 " d4, ζz 7 *4d,4 ζf " d4 ζd R*4d,4 " d4,W ζz 7 >d4 ζf " d4 ζd 8d4 ζz 7 >d4 ζf " d4 ζd ⇔ 8ζz 7 >ζf " ζd ζz 7

>ζf " ζd 8

6>8

Kce{lnhtfenc'{h vxh c kcha lklhe~h lklhe~h nh nlif~fíëc kÿdlkf nc kctpc h c nc içvxlnc {ëc th{phk~lqfghe~h lmxfl{ f 6: ½ 60‛1 °K‛6 h ;10 ½ 60‛1 °K‛6) lenl' vxh f cpíëc hg vxh {h hekce~tf c qfict fptczlgfnc nf ~hgphtf~xtf hg vxh {h næ f ~c~fi lght{ëc nc kctpc% f, 41< °K% d, 4<> °K% k, ;6< °K% n, Eëc jæ ~hgphtf~xtf pc{{çqhi pftf vxh c nh{ktl~c ckcttf% h, ‛41< °K% Th{cixíëc?

PARTE I – TERMOLOGIA Tópico 6

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