Introduction to Physics I

Kinetic gas theory- equipartition, degrees of freedom- mean free path- Maxwell-Boltzmann distribution- Brownian motion

Ideal gas examples: adiabatic processes

Real gas law: van der Waals equation

L23, 08.12.2017

mean free pathcollisions for a moving molecule

Tipler

mean free path, ideal gas at STP

Hyperphysics

STPstandard pressure & temperatureP = 100kPa (1bar)T = 273.15 K (0C)

Atomic diameterassumed here0.3nm

measuring the speed distribution of molecules

Tipler

Maxwell-Boltzmann distribution

Tipler

equipartition theoremdegrees of freedom & molar heat capacity

equipartition theoremdegrees of freedom

Tipler

H2

equipartition theoremheat capacity of a solid

Tipler

(Makro-)Mechanik

Temperaturschwankungen:

xth = 0.2 pm = 2 x 10-13 m

T = 21 °C

Temperaturschwankungen:

xth = 8 nm = 8 x 10-9 m

T = 21 °C

Nanomechanik

adiabatic process

Tipler

real gas law: van der Waals

Tipler

real gas law: van der Waals

Uni Bristol

PV diagram PT diagram

real gas law: van der Waals

Uni Bristol

PVT phase diagram

real gas law: van der Waals

Tipler

§r*-b. l*ol ,f a"*Lr? (

@, Lr[- <r7o.r,l) C«f . ]e-kc6q (L"l) wl.s l, ,).n

e a \rL,huu L", 4 a*n_ri,^ c, tf.,l, .1,*"1(ay"Ayt.l= j , Lri,t o,t,,L.h^q

4k* 4"t (w,r,"crhw;")

' tr-v.iu[a :

r,* L". C^,

t wt,t lr, "(

A Ca= Ç, rsT

ai,Ll ;Aa= c,u^ Âl

l/(h*l( c

l-,,lah',,,,1

ItuLcrcittry t

tuÀ{[( (nr-,

lü* +t- inkr,ol ei^c.t- ol-_v/ J

ü,"ok, cun r T

N (t "u1,,

t, ocrn,volo-L h ,'r..or.

àr)

ls eâ. 4 !,,-t".--l I\i,.r = j rn; = F,nr

ff;n!;td*'l'.

ub t'zh-

F,'", hu'. H., LuL co/r,r,lç t,, L.

.) à6.a-,',, = -,d,

il'"'{"t(*L*at'y" *,* jt ,,,+r,, voluw)

dt-iu 3 ,-- 'i hK

dt

,é" d" L"^t opt,i,l7

fuÔ, d, ,L qn,l, volrw,- 7

4 u"v'' :i',;::,*'r*i'.!,'*;" 1.1;?'

V{_g",1 1 q<ïtut;ou, (attrtwu /= !r,, ty , kat, ÿl"u

"d&l Ë, tru, l*, E "ld yewLur,- (y!diW . T.,15 =P.+,/J = ?.d,V

,"1ï ,l dV=o r ;t c)U/=6,

%-,lf - Cr.àr : Pdv

*r?I ? àV= ,^.Q.àT{t sl-b e7. ?V "

ct-Cv

nnlt ( l*u"),,

l**t d C<

10.v1 ,I *'t,

- l, ru I-_ vÿt

. i,t"- ?

artrll , lrarLonl

il r,r^/

("

i*«

=r(trÈ . f,nR

u'PL

Cp = Cu* Cv=

o, idlul tur,walowt, qot( d'

êQ - un-tA v\

L. kou,[uhou.l *oLl"--

{laon-, .'[ u t,i oln,.,

trr &

Ç.t.,"t tt,1,ti.\

u, vL "J*t \, veq "f sa.pL {3rt*r.,1l).t vnolo, u,,,' LnJ "*/

hn ; ,h f". wou*lau", (g/>4 (*J*"1), *[*,,LuJ,

t"Ll 9tt u"J.t(et /d.ÿ

= svL. )

1r,*

,?ry )

' l-t

ù cJ l.- vt,a'c,t4, r^cL',uÇ

I " c<.,-pr,,z wa1*J yub. t

Fehne r^L. ,, f rr l.,b,^ woclu

(ohf" à"t J, ü.'u

l-rrl. .,l.E,"*- 18n., , LEu,,

gL

ikot r^t(l_,- tt./l(4Pt"

,-J pl ek.yà\==_1 ,-_ v,\. '- _u,1, l

1 Lf," ' )- Èpt /[t ,. L ê ,t\ îr"' lü

we,6hr /.

.§Ao'

, r"rn: lo'

- q' &' ilt ' &ul-l'", "l 'oL'fi"- ,.od'n

w 1- wdk a) *,9,"È *[*[-l sL.,L ùrco*u)

l:}aad, v,\çsln, u

d4, uÀ"" ç,r-,5')1",*et. iI-c

c(v;\ ct.+R

-r,._./

U"

[Zr"

u

I Jlotr'ri CtLtgu'n*t U

u,ly,l,t,-

(,,

4".

It unr,,no al.,w,,.- 3 'l,A lr*k^ (l'-u,)

i

L. = 3.1r2 = iRv ') -')

)Jr, à;^lr,^, i àu,, ZroL, l;;lt" (=6l-,'! r1,l', v,l'

ttc, =(:*z+Àt-,t) lt=ZR' lt î' 1 2

kr'r Pof

.C0, ) 3kuv^,2*f $v;\, (=&

C,'J3,-LrL.u)4À= If-\ /1 1

ç irlrr. ?oü k

,]

-ry\ â,r

/-f ""4"2t1'tvnb t"l\.2 1-y .' 1to1 ," ,y4 )

n,l-"d"ta :"1

,! 1"rk ,o,r,Tt

[" 1,]" "x 10

^to"J" fq'r\r 't

'\o) 1Y'C - çn^lnq

?1 = ;a ll

J'à e = !è'î '2 JVr"a

--f"ol |" BV g , .r1y

,-W,,-3\,e",d, qt,,1 n"JA,l)

l" f1,rt n,"l ',$-ij, , ll'ylpl'noj1-0,,n

'J "r 'l

\ r'tl"rt '4

-? ['4--f -, , "

, l. Z tla ? - Z / L

i) Lh tt'h1 ,

.x à i r rV4l . t'n.4 i .r '"41 s ,?n*f ,

"on. i - i"^T --r'l

fp f 4P»"ra ,,-"1n,r l"TI

Y;Y' h (t^/' yl + tla 1 tnol».,ÿ^!','

4 i -1ü ", .' zlyott f ,-1- l" qo4a1q ovl

lnt-ry. 1. y,t,1 -n I&,rao1;r| -y l, ."qnln1 'v

;l,r,rnnofo4,^a",ttz;d

/'(r1 . .,*7 "r^-{l

?ir{or^

i"'ulqlt s.rrfu )

trT\?

ohLll

(Ztbtr

lwG,t )u ubs,L Y+-th or a'r- t ol c\ sÿrtch Crl,, W hu,ÿ-rei

((','- lttut o,a .) {r, ,

aa=o)

P r-- , t?.1-*,\ f ,l.tl;a,'iXu)

n j,',rL b, lk,* i

df,,r = q df

t"n lobÀ -(or^Line,-

6rI),4,ltubuh"

tll\h

Pv ù,5'""

ah|-L = )G.,- . au,,

:o,adt"L"Æ. prra+§.-ea 1ndou,l1 t

(Lto - c2..1co",l. 1/.LL,L c1u,il, ,r

ol uo,^. -?àv

ÿl^u-,

tuLôraq

an,l

là",

(n",

lr l,rk d,* uu g*0U..u,alrr,lth. p,t,u.

JC,r.rlî= o *9rlvadr+ n_t dy="

v

{ * n'R.N,6lcrv

l"-| Ê 13.it( =çruç)'C.v

( ?.rt. ^u ,

)

t_tr^ ( i .

Ttÿ

oJÿ-U>

I§_Cv

ln v nÿo

v'u/') - @ut!-

nk/ç

ICv

= 6ruaf

CD-C. = hPt.

ltlwt'bualuw r 4<'t,

t-r

cr, ty[* L.l,rbt'tP

'? -4 -e

"{ ru, ut)

lllu. Lou .

ün,, Fü,= rG-î

a*l @., a)t,

o

fi

Lld *'

= cout l-

,l

T?.uurl

.''r"-

\V

?.V ,,1- (_ - v - rtttoIL' h[L

ll P vt= «,u,,t

' (aL n'ro'l"i

Coc rL

l. 9.Cy

îa, w,,t*h-, (ilrl,t 4.r, )

(.5 . ttt'r *Lt"/ oyl#u ) +Sf nt\,,tr""

rlCrCn; , 6{y6<,. -eunLL{ ai, (tt;1,.r1d-g Jt,tvg : oÿ1ge,-. Ll,u,.n (t^.1,,,^)

(orrid ü,ioJ..^ t N Lü! r,f-

("y' )'"'-

i{ ur*6* c'(lra;^l{7 dilrt, (i^ coul;*l cJu^- v),eac[. 6a", ocrapb fu* u[o! ,oluu* l/ /

( Vol "J Stt y,oLt,+L, wat,y\1, d, co1x,d # V )il* P",r6u,. ' Z ?, , 'u* 'l t'n')'L;tlu.'l ynx(,,c"

=ff Ln;Rr

o@

I'uL d rr^"1. |",L'".âo"l

do*t

d

6

tr,lrobnb,-7,

&

Lrctwwa,^t-

It " h'oe" ; ronÂo* Y^eon-tpwL 4 ,.1",v1c-y:c'

pr,. À,-L §u.,pr^lcJ i- a b1u'l o' aEo'/

Ltr( \6

,oc) ÿ -41t1 p,u l'ttL - 7,"L) ;b/tt*I t

' at'"*lqÿù" lvat'al't

( L> dr,*l'un*,' slr""ç^* 4'*A)

(

(

fi"t*t B.rn kz? )b" Lur,ierptuako' ,Êi,,1,,, ,Do; 1,t (L,^.t^lnrr*.-

fcru P".";-, E...[.Lh* g"*ut',u

- §iu.o 1.. po^ {'". U i' at/

* lo u,n - 4/b

tr LOo6.r^ { lortr,,w'r^rn tuohov : /l ifl..'i "1 y"kL iv éào)l0r l

l[ O*à opo].l dl^"o^' w:ll ,,u'Ç.uJ ") 5''

' F,'r, /.i" '- ,br,*,on ^iî o' u't e't''Len'* ("t fL'o*'rË.- .t[ '[o*' (a'Q-L/

| 1", )" 7*n't:')4'Ë* /1t"' ill I

| *' - '[ eLl'"" P2otD /

0 Àt[l^r"^ cau'hÿ'[) f Ô] - #'8,'> 'Iv D'{-u,â1t

l,l11or,, ''*bytlonL

( sLW! foâ,nG4k".,,L

-+ l^r1,H",', f'enplouoto'

ULI,I"^'' L

D,lorh.-

cs,rLl,"/ -81,,8"4[?",r, s,[d.,: ri.-| 't,à.

O,^ r{

- 1,1,.tra tuu,\.oaîu/

- ttcrrao [gaLarü y

1 yu'k"

arç po.[',Lûr,u hor^

D. lrn.i f" ffhtB

[+^ù)*t'{ r,r'1.\

r,r^o, "j "6r.\*, y*-s4 #*

fO,, "1, *

o)ul^'o,,1,^t1 W"-,a wo.trv tnytr,l,{r*a(oa.,k* &.'^À U,* altv^,u

wl"*-/ f-yb- 'lW+t<r'

Çlibr- ,o*;,Là"rfl- u^.ffi^ -1. "^,llJ-ICLÀL(à qu-<- ro

ÿvsuiut J"ryt"S o^tr,/

+1,1.

Cngfi

1vixogl,q

,[1,y4

( r')- ./0

1,3.T'+

6$o'R

Q!(q.-?.

-r----.

È-- l -------=

-r-- l +:*+

IJPiqutlF.7 ,l 6os *0t ."t"

Ç.tr;;;f"-r;iu c,"46,,,-, . - -:-Eie"TÀ-,I -r, :' t+l-ul< -- V'.-,z !44

FË-- çt a! - - "!

-t'1) I I I lt.-& u l0 j . _ttw, tlettt -zt- ç"Lk ho-/

(

,rcritéÈ]lù- . tr;; il- .

- - : - .--- -ft.&r;;I- d"; Ltï.. ;tr ',";hÇ-t il-eeul-tr+;- -

. _ ,-,_- .' . _-=_. . (.:,nl44.üt;[t* [.4_«Jidffi-J '". __ -_ .

luilùf,"1ÿX* - Lr&- - - - .- "

i;l / -'

ù.-Ê.L

': .-.:: -- -- - : -- ---,--. --.-.- i^!--l i",ffiL,J;4+i t§;,b&-!*,-i;t[,f..-t LéL h:v-, . il

t,'\', .\

t.''r:""- ''

'' l '-

'- '. ,u

' -*- ..-- -- -- --;'-pta1

rrg..ti.ç.