Basic Thermodynamic Relations

Transcription

1 Basic herodynaic Relations Isolated syste: this is a syste that does not exchange energy with the surrounding edia. First Postulate (equilibriu theore) : Isolated syste always reaches the equilibriu state and never leaves it sontaneously. econd Postulate (teerature) Every equilibriu syste is coletely deterined by the set of external variables (volue, ressure, agnetic field, etc.) lus one internal variable EMPERAURE. At least one additional internal araeter is needed to describe a non-equilibriu syste. Equilibriu Process: his is a rocess that roceeds so slowly that the syste is always in equilibriu state

2 he First Law of herodynaics he First Law of herodynaics is a stateent of conservation of energy in which the equivalence of work and heat flow is taken into account. du dq + dw he internal energy of the syste U deends only on the actual state of the syste and not on the way the syste is driven to it, i.e. it is a function of state.

3 he econd Law of herodynaics Efficiency. his is a easure of how well the heat flow fro the hotter theral reservoir is converted to work. If the work done in one colete cycle is W, then efficiency η is defined as the ratio of the work done to the total heat flow Q η W Q One of the ain consequences of the econd Law of herodynaics is the existence of another function of state called entroy d dq Processes in closed systes are always connected with an increase of entroy. In equilibriu the syste has axiu of entroy.

4 d du + dw for dw d d du + d Free energy For oen systes dw ( du d) F U G H W ( F F ) dfdu-d-d-d-d (for const) df d d

5 Basic herodynaic Relations First derivatives of herodynaic Potentials: F F G G,, O G O F σ,,,, n H n U n G n F µ

6 econd derivatives of herodynaic Potentials: Heat caacity v F c coressibility o o F P k G c o o G P k heral exansion coefficient P o α

7 herodynaics of Phase ransitions Every hoogeneous art of a heterogeneous syste is called PHAE. Phase is a acroscoic, hoogeneous, quasi closed art of a syste, searated fro the other arts of the syste by a searating surface. According to the lassification of Ehrenfest the order of the hase transition is deterined by the order of the derivative of therodynaic otential that jus at this oint.

8 heral equilibriu α β dq d α +d β 0 dq α + dq β α β 0 Mechanical equilibriu (at a b ) Pα P β df α +df β 0 d df -d d (d0)

9 - α d+ β d 0 α β α heical equilibriu dn β At,P const the two hases exchange aterial dg α + dg β 0 dg vd d + Σµ i dn i -µ i α dn i + µ i β dn i 0 µ i α µ i β

10 For the first order hase transitions: In the transition oint the cheical otentials of the two hases are equal µ g P const It is seen that I order hase transitions are accoanied by a heat transfer DQ ( ). he heat of hase transition is the heat required to transfer substance fro state to state. he axial work is W ax (DF) DQ - (DU) Q

11 he Kirhoff equation gives the teerature deendence of the heat of hase transition in differential for Equation of lausius-laeiron µ, ) (, ). () ( µ dµ(,) dµ(,) or µ µ µ µ d + d d + d o that d d s v s v Q ( v v ) Equation of lausius-laeiron For the second order hase transitions: In the transition oint the olar enthalies, the second order derivatives of therodynaic otentials of the two hases are equal d s s d v v L Hoital ds d d d dv d 0 0? ds d dv d c dv d

12 d dv d dv d dv d dv d ds d ds d d because s P v µ Ehrenfest Equation k α UPERAURAION D G ( )d µ d d 0 d d µ note: ( ) d

13 herefore ( )d µ A truncated aylor exansion of () in the vicinity of gives: ( ) ( ), + o that suersaturation becoes, µ, H µ exale: for const ( ) H ln + µ

14 Nature of Glass ransition: exeriental evidence glass µ liquid (undercuuled elt) crystal tructure PMMA lgη [Pa.s.] /

15 63 Heat flow [W] eerature [ o ] 3,5 3,0,5 f g,0 ln(q),5,0 0,5 0,0-0,5,5,5,5,5,5,53,53,54,54,55,55 000/