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Xin trân trọng cảm ơn!
Thanh Hóa, ngày 16 tháng 05 năm 2013
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,WAGd<‡E˜<BIG&|@
_VG
_VG 2BU G
T c
pV c p
=
= → →
;%&'=>"K1 !Vbiểu diễn đẳng quá trình sang một hệ khác.
d<Px>NEwG<mPBTWRBr?A?ZWAGd<PBYEjBGsG<AB?bUXG
>[•S<^G_<IŠh‹Fi@
hkGCZWAGd<PBYEjBGs
G<AB?b>[•S<^Gx
Ph6BTWRBr?A?ZWAGd<PBYEjB
?<]GS<^G_<IŠ2h‹KNŠh2‹
FG"# q"
žZWAGd<|@2ˆ?_VG@E˜G^?<
Gv @ →WgE˜G^?<
Gv @Wg
žZWAGd<|@ˆ?_VG@E˜<BIG
BCU @ →BFfE˜<BIG
2Gv @BFf
žZWAGd<|@ˆ?_VG@E˜AD
BCU @>NU>s< →>NU>s<E˜AD
2BCU @‡ →‡E˜AD
P"<WiTV<IŠ2h‹KNŠh2‹
ž,WAGd<|@
›4s@2ˆ?_VG
›4s@Dˆ?_VG ŠDG•>IG<WQKLB‹
ŠGvhGv‹
,WAGd<|@
›4s@ˆ?_VG
›4s@D2ˆ?_VG ŠDG•>I<m?<KLB2‹
ŠDBCUh2Gv‹
&
2
2
,WAGd<|@
4s@?_VG
4s@2?_VG 2G>IG<WQKLB
BCUh2BCU
)
2. Giaới phaùp 2:
Bióứu dióựn caùc quaù trỗnh bióỳn õọứi bỏỳt kyỡ cuớa chỏỳt khờ sang hóỷ
khaùc.
M[bk',B^]'V
|Œ*KQG>{?<•Ry>sBfKBI?•‡G?A?E˜ZWAGd<
›˜AD
›˜G^?<
›˜<BIG
|?gG<TUfX?<_ZWAGd<P]GS…ZWKBI?G<H?<BI?A?P[L?VW@
s;FG.@•A?Em<ZWi>WQGPBYEjB?b?<]GS<^P„D<[\Gd<G_A
<a?ŠGyEwG<mVWi<_o?RHKN_?A?R`SBIEMPNB‹@ŸŠh2h‹ˆ"
s;FG.@<N<>QD<ID<[\Gd<
ŸŠh2h‹ˆ"
Šh2h‹ˆ
pV
T
ˆ"
ŠD<[\Gd<GsG<AB‹
*<€G_G<kVJGy<IGxGE[•?UXGD<[\Gd<>Bx<IB`
<BG<kVJ?t>sB@<Ših•‹ˆ"
<iiˆŸŠ•‹
›;FG.2@*<C_VAG<NUVJiˆŸŠ•‹GK‚E[•?EwG<mG_<IŠih•‹
•∈ h2h¡
i∈ h2h¡h•≠i
• YWPBTWRBrG_<IŠh‹G<dGS<€G<kVJ2
• YWPBTWRBrG_<IŠh2‹G<dGS<€G<kVJ
• YWPBTWRBrG_<IŠ2h‹G<dGS<€G<kVJ
) !"##&<&.>. p"#'=>"
;%&'=>"K1 !V
"<_PBYGUXG>[•S<^PBYEjBG<l_
UXGZWAGd<<[EwG<mPx
FiPBTWRBrZWAGd<PBYEjB?b
?<]GS<^G_?A?<IŠh‹KNŠh2‹
FG"# q"
|<Q•‡G@,WAGd<|S<kD<CB>N?A?E˜ZWAGd<
→S<kG<TV€R=E[•??A?D<[\D<ADG<kG<[n
|yEwG<mhG?gZWi>WQGPBYEjB?b?<]GS<^@
ˆ2 ŠˆGα@>N<IVJg?‹ Š‹
¢
|<[\Gd<GsG<ABS<^>^G[f@
pV
T
ˆ?_VG Š‹
.
2
6BTWRBrG_<IŠh‹→S<€G<kVJ2
GyŠ‹KNŠ‹hG?g@ˆŠ
_VGa c
‹
→ˆ"
>N<NUPQ?<B?bxEwG<m>NUXGD<c?bDP_>Š<d<K‚‹
P6BTWRBrG_<IŠh2‹→S<€G<kVJ
GyŠ‹KNŠ‹hG?g@ˆŠ
_VG
a
c
‹2
→ˆ"
2
>N<NUPQ?<B?b2xEwG<m>NUXGD<c?bDP_>Š<d<K‚‹
*Ghi nhớ kiến thức : Hệ số C
1
≠
C
2
nên độ cong đồ thị là khác nhau.
;%&'=>"K1 !V
"<_PBYGUXG>[•S<^PBYEjBG<l_UXG
ZWAGd<<[EwG<mGxFiPBTWRBrZWAGd<PBY
EjB?b?<]GS<^G_?A?<IŠh‹KNŠh2‹
FG"# q"
ž,WAGd<|@
›4s@2ˆ?_VG
›4s@ˆ?_VG ŠGvhGv‹
ž,WAGd<|@
›4s@ˆ?_VG
›4s@2ˆ?_VG ŠBCUh2Gv‹
ž,WAGd<|@ˆ2
Š‹→ˆ"
hŠBCUh2BCU‹
Š&‹→ˆ"
2
2;%&'=>"K1 !2V
ŠWiTGQDEMG<B/>iUDB?|&KQG>{>cG<q2‹
[nBG?<qU<l>BG_UXG•B
7
2
2
2
2
2
2
><?gD^GGkS^wB?<_>[•S<^<l>BEg
PBYEjB?<QU?<sDGyGsG<AB?gG<TG^?<
2
ˆ>BGh
ˆ&hGUVGsG<AB?g
G<TG^?<2
ˆO>BGh
ˆ)h)GUŽB<BIGEX>L<]GUNS<^EsGE[•?>NP_
<BxW£?<_PBYGZWAGd<PBYEjB?b?<]GS<^<[<d<K‚
FG"# q"
DVW]G>N<NUPQ?<]G?bG<TG^?<2
ˆ2›P Š‹
<l_BCG<BYGhG?g@
ˆ2
›P &hˆ›P ˆ|h)
ˆ2
›P→ )h)ˆO›P→ Pˆ
oGS<A?hG?g@
2ˆ
m
µ
ˆ?_VG Š‹
yŠ‹KNŠ‹VWi@
2
›P2ˆ?_VG Š‹
<i@ˆŸŠ2‹
wG<m?bD<[\Gd<Š‹
>NUXGE_sDP_>EBZWJ?
GaEXhPM>’UZWi•WJR[LB
*<BEsG<BIGEX>L<]Gg?<BYU@
<TG^?<@2
U•
ˆ
b−
ˆ>
ADVW]G@
U•
ˆ2
U•
›PˆGU
2Qi
U•
ˆ
U•
2
U•
m
µ
ˆ&O*
2M[bk',B^]'V <[\Gd<GsG<AB?bS<^>^G[f@
pV
T
ˆ?_VG
:
2
2
U•
2&<&),>)2V
t !"#*+',-=>",.>.',u"#f'Ap"#',>&
$v"#.>.,Kw',m@.>.*h"#iB>'AC",
Œ€R=<IVJg?h•A?Em<EXRJ?
2NB>'AC",*h"#",&e' @
ˆ
_VG
2
T c
›,WAGd<E˜<BIG
@
ˆ
_VG
2
T c
ˆ
2
a
›,WAGd<E˜<BIG
@
ˆ
_VG
2
T c
ˆ
2
a
YW
‰
→
‰
→EwG<m
fGx
Š<d<K‚‹
2NB>'AC",*h"#'1., @ ˆ
_VG
2
c
›,WAGd<E˜G^?<2
@
ˆ
_VG
2
c
ˆP
›,WAGd<E˜G^?<2
@
ˆ
_VG
2
c
ˆP
YW2
‰2
→P
•P
→EwG<m2
fR[LB2
Š<d<K‚‹
22NB>'AC",*h"#>) @ 2ˆ
_VG
D
c
›,WAGd<E˜AD
@
2ˆ
_VG
D
c
ˆ?
›,WAGd<E˜AD
@
2ˆ
_VG
D
c
ˆ?
YW
‰
→?
•?
→EwG<m
fR[LB
Š<d<K‚‹
2>) !"##&<&.>. p"#'=>"
2;%&'=>"K1 !V
d<PxPBTWRBr?A?E[nE˜
<BIG?bUXG>[•S<^qKLB?A?
<BIGEXS<A?<W
h
"
•
O
2
2
2
2
2
FG"# q"
>.,@Œ€R=RsD<[\Gd<G_A<a?
<[\Gd<GsG<AB@
pV
T
ˆ?_VG →ˆ
_VG
2
T c
ˆ
2
a
›[nE˜<BIG
@ˆ
_VG
2
T c
ˆ
2
a
›[nE˜<BIG
@ˆ
_VG
2
T c
ˆ
2
a
2dE[n
fGx
→
‰
→
?_VG‰
?_VG
→
‰
ŠED?U‹
>.,@
|2‚E[nE˜G^?<?‘G<BE[nE˜<BIGGsBKNŠ<d<K‚‹*<B
EghG?g@
p T
p T
=
•ŠKdK•
‹ →
•
ŠED?U‹
2;%&'=>"K1 !V
d<PxPBTWRBrE[n
E˜G^?<?bUXG>[•S<^q
KLB?A?G<TG^?<2
h2
"@2
‰2
FG"# q"
>.,@
<[\Gd<GsG<AB@
pV
T
ˆ?_VG→ˆ
_VG
2
c
ˆP
›[nE˜G^?<2
@ˆ
_VG
2
c
ˆP
ŠP@>N<IVJg?‹
›[nE˜G^?<2
@ˆ
_VG
2
c
ˆP
2dE[n2
fGx2
→P
‰P
→
_VG
2
c
‰
_VG
2
c
→2
‰2
ŠED?U‹
>.,@
|2‚E[nE˜<BIG?‘GE[nE˜G^?<GsBKN
*<BEghG?g@
p V
p V
=
‰ŠKdK‰
‹
→2
‰2
ŠED?U‹
2
2
2
22;%&'=>"K1 !2V
Š^?<EMG<B<a?VB<BŽB>LDvU<a?|&‹
wG<m<d<PxUkGCUXG?<WGd<?bS<^>^G[f
Fi?<•Gx?<WGd<@
|"A?EBTU?bEwG<mqKLBADVW]G>L<]Gh<Ž<]G
|"A?E_s?bEwG<mqKLBADVW]GGvhBCU<_o?S<kEjB
FG"# q"
|•‡GUXGEBTUP]GS…GxEwG<mhK‚E[nE˜AD/Š
‹
IVJg?E[nG<˜/>N@G
M
α
ˆ
M
M
V
T
|yD<[\Gd<GsG<AB?bS<^>^G[fh
?g@
M M
M
p V
T
ˆ?_VG
→
ˆ
_VG
2
c
ˆ
_VG
G
c
α
Šž‹h
•
M
α
•O
|yJ?GaEX/GS¤GBYDGWiYKLBEwG<m@/KN/6
*<i âoï@
α
6
≤
α
≤
α
→G
α
6
≤
G
α
≤
G
α
→
6
≥
≥
→
U•
ˆ
6
h
UB
ˆ
|BGBYDGWiY?<BKtGtG<N<?W
›Gx?W
6h?<BMWPBYEjB?bZWAGd<>N→
→6@
α
BCU→Gv¥GyŠž‹
›Gx?W6
h?<BMWPBYEjB?bZWAGd<>N6→
→@
α
Gv→BCU¥GyŠž‹
26;%&'=>"K1 !6V
B•i><?<q<B>_sBS<^?gS<JB>[•U_>
µ
J
µ
S<A?<W<[?ƒS<JB>[•UhADVW]G?b
?<uP„<W,WAGd<PBYEjBE˜ADE[•?
PBTWRBrPfBEwG<m<[<d<K‚
Œ_VA<?A?S<JB>[•U_>
µ
KN
µ
FG"# q"
y
K‚E[nG<˜V_V_/2h?‘G/
µ
h
/
µ
>c>[•GGsBKN6
DR=D<[\Gd<?>|Dx|k|l|Ex|>x|‡DGsBKmG^KN6@
/
2
µ
µ
6
2
2
/
2
µ
µ
2
6
6
m
pV RT
m
p V RT
µ
µ
=
→
=
V
V
µ
µ µ
µ
= > → >
2x;%&'=>"K1 !x V
XG•i><?<qS<^Pm<fxS<^?gG<T<_o?
KN_•i><?<QU*<BADVW]GDS<kEjBhG<TG^?<
2PBYG<BxG<l_<[EwG<m<d<K‚ŽB>[•
S<^G_•i><Gv<iBCU
FG"# q"
y
K‚E[nG<˜V_V_/2?‘G/
GsBh?‘G/GsB6<[<d<K‚
m
pV RT
m
p V RT
µ
µ
=
→
=
m V
m m
m V
= > → >
6&<&),>)6V
t !"#*+',-=>",.u"#K%",&e'.,/'0,1'AE=*j&
'A="#.>.iB>'AC",$&]"*j&'Ap"#',>&
/
2
/
2
6
2
2
6M[bk',B^]'V
6BTWG<q?Wix>{0@
U A Q∆ = +
h
Š ‹A A A p V= − = − ∆ = − ∆
∑ ∑
Š ‹U f T=
*<BE\KmŠD‹h2ŠU
‹G<d?kŠ¦‹
"<]GS<^RFfVB<?kG<d•
6NB>'AC",*h"#",&e'V
•
T T U U U= → = → ∆ =
• 6BTWG<q?Wix>{0@
A Q Q A= + → = −
• X>L?k@
A =
4BIG^?<<d<G<?_2
2
6NB>'AC",*h"#'1.,V
•
V V= →
h
Š ‹ A A A p V= − = − ∆ = − ∆ =
∑ ∑
• 6BTWG<q?Wix>{0@
U Q∆ =
62NB>'AC",*h"#>)V
•
p p= →
Š ‹ Š ‹ Š ‹
M
A p V V R T T R T T
ν
µ
= − = − = −
• X>L?k@
A =
4BIG^?<2
2
• 6BTWG<q?Wix>{0@
U A Q∆ = +
6 AÏp !"##&<&.>. p"#'=>"
6;%&'=>"K1 !VXG>[•S<^E[•?RFGyG<TG^?<2
EYG<TG^?<2
Š2
‰2
‹Œ_VA<?kS<^G<H?<BIG_?A?ZWAGd<@
‹˜AD
P‹˜<BIG
?‹4FE˜ADwBE˜<BIG
R‹4FE˜<BIGwBE˜AD
FG"# q"
2ŠU
‹
ŠD‹
2
2
ŠD‹
2ŠU
‹
2
ˆ2
ŠD‹
2ŠU
‹
D
ˆD
2
2
2
2
2
2
2
2
2
2
2
2
2
2QR=SBYG<q?
A =
4BIG^?<2
2
hG?g@
‰
?
‰
R
‰
P
6;%&'=>"K1 !V
XG>[•S<^>^G[fS<kEjBfGsG<AB?gG<TG^?<2
hADVW]GD
h
RFE˜<BIGEYGsG<AB?gG<TG^?<2
ˆ2
ŒWEgRFE˜ADV
GsG<AB?gG<TG^?<2
ˆ2
‹2‚EwG<mPBTWRBr?A?ZWAGd<GxG_<ID|2
P‹4ƒEwG<mETV_VA<?k?bS<^G_?A?ZWAGd<Gx
?‹2QR=Wix>^0D<eG^?<VHG<iEjB?bXBvKN
<BIG>[•?<]GS<^G_EjBKLBUkBG[n_NB
FG"# q"
‹2‚EwG<m
P‹"v?qRBIG^?<?A?<d<hG?g
‰
?‹ž•‡GZWAGd<E˜<BIG|@
T T U U U= → = → ∆ =
2
‰2
@?<]GS<^VB<?kxˆ|
h
•
<l_Wix>{0@
A Q Q A= + → = −
‰
Š?<]GS<^<Q<BIG>[•GyPx_NB‹
ž•‡GZWAGd<E˜AD|@
2
‰2
→
?<]GS<^VB<?kxˆ|
h
•
2
‰2
→
‰
→
‰
→
U∆ >
@XBv?<]GS<^Gv
<l_Wix>{0@
U A Q Q A U∆ = + → = − + ∆ >
@
Š?<]GS<^<Q<BIG>[•GyPx_NB‹
62;%&'=>"K1 !2V
"gh&U_>?<]GS<^>^G[ff<BIGEX*
WgS<^E˜ADEY<BIGEX)*h<BIG>[•
?W?]D?<_S<^G_ZWAGd<Ai>N>N¦ŒW
EgS<^E[•?>NU>s<E˜G^?<EY<BIGEXP„<IG
&
2
2
2
2
2
D
2ŠU
‹
ŠD‹
/
2
EXPEcWKN?WJB?ƒS<^E[•?E[GfKMGsG<ABPEcWP„ZWAGd<
‡E˜<BIG
‹2‚EwG<m?b?<WGd<G_<IGaEXD|2
P‹^<?k
h
UNS<^G<H?<BIG_ZWAGd<E˜AD
?‹^<EXPBYG<BxXBv?bS<^fU•BZWAGd<?b?<WGd<
R‹^<<BIG>[•UNS<^<QE[•?G_ZWAGd<E˜Gêch.
FG"# q"
‹2‚EwG<m
P‹^<?k
h
A
S<^G<H?<BIG_ZWAGd<E˜AD
h
Š ‹ Š ‹ Š ‹
M
A p V V R T T R T T
ν
µ
= − = − = −
ˆh&:hŠ)|‹ˆ):h7Š¦‹
?‹^<EXPBYG<BxXBv?bS<^fU•BZWAGd<?b?<WGd<
DR=Wix>{0@
h
U A Q A Q∆ = + = − +
Šˆ|
h
A
‹
žXPBYG<BxXBvG_ZWAGd<E˜AD@
h
U A Q A Q∆ = + = − +
ˆ|):h7›ˆ&:hŠ¦‹
Š ‹ Š ‹U f T f T∆ = − =
&:hŠ¦‹
žXPBYG<BxXBvG_ZWAGd<E˜G^?<@
h
U A Q A Q Q∆ = + = − + = +
Š ‹ Š ‹ Š ‹ Š ‹U f T f T f T f T∆ = − = −
ˆ|&:hŠ¦‹Š
ˆ
@E˜<BIG‹
žXPBYG<BxXBvG_ZWAGd<E˜<BIG@
Š ‹ Š ‹ Š ‹ Š ‹U f T f T f T f T∆ = − = −
ˆ Š
ˆ
@E˜<BIG‹
R‹^<<BIG>[•UNS<^<QE[•?G_ZWAGd<E˜Gêch.
h
U A Q A Q Q∆ = + = − + = +
→
Q U= ∆ =
|&:h¦•
→
"<]GS<^<CŠGWiM‹<BIG>[•Px_NB
,!b!.V>.$%&'()K(" !"#
;%&'()K(" !"#V
d<Px>NEwG<mPBTWRBr?A?ZWAGd<PBYEjBGsG<AB?bUXG
>[•S<^G_<IŠh2‹Fi@
)
2