O segundo e terceiro O segundo e terceiro principios da Termodinámicaprincipios da Termodinámica

Cambio espontáneo: Aquél que tende a ocurrir sennecesidade de ser impulsado por unha influencia externa

Rudolf Julius Emmanuel Clausius(1822-1888)

“Der Energie der Welt ist konstant;die Entropy der Welt strebt einem Maximum zu”

A entropía e o segundo principio

T

qdS revδ=

dS> 0 proceso espontáneo nun sistema illadosistema illadodS=0 proceso reversible nun sistema illadosistema illado..

S é unha función de estado

∆S = S2 – S1

T

qdS

δ≥

Ludwig Boltzmann (1844-1906)

Interpretación molecular da entropía

S = kB Ln W

Microestado: Disposición das partículas nos distintos niveis de enerxía

Macroestado: Estado observable caracterizado por un conxunto de variables macroscópicas (n, P, T)

Duplex Solomillo Perete

W = nº microestados compatibles cun macroestado determinado

3º Principio da Termodinámica3º Principio da Termodinámica

A entropía de todas as substancias cristalinas

perfectas é cero cando T=0.

O cambio de entropía que ten lugar en calquera proceso físico ou químico achégase a 0 cando a temperatura achégase a 0 sempre e cando as substancias implicadas estean perfectamente ordenadas.

Walther Hermann Nernst (1864-1941)

Max Planck (1858-1947)

TTT

HT

TT

HT

TS

298

T

(g)p

ebull

oT

T

(l)p

fus

oT

0

(s)po

298ebull

ebull

fus

fus

dC

dC

dC vapfus ∫∫∫ +

∆++

∆+=

SSS

r

N

i

ii

PT

∆==

∂∂ ∑

=1,

νξ

Entropía de reacciónEntropía de reacción

T

C

T

S Pr

P

r ∆=

∂∆∂

Variación coa temperaturaVariación coa temperatura

J. Phys. Chem. B, 102 (40), 7871 -7876, 1998Web Release Date: September 12, 1998 Copyright © 1998 American Chemical Society

Heat Capacity of MgSiN2 between 8 and 800 K Richard J. Bruls, Hubertus T. Hintzen, Rudi Metselaar, and J. Cees van Miltenburg

Centre for Technical Ceramics, Laboratory of Solid State and Materials Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, and Debye Institute, Department of Interfaces and Thermodynamics, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands Received: March 18, 1998

Abstract:The specific heat at standard pressure (Cp) of MgSiN2 was determined by adiabatic calorimetry in the range of 8-400 K and differential scanning calorimetry in the range of 300-800 K. The measured Cp data for T < 24 K can be described using the Debye T 3 approximation: Cp = aT 3 with a = 1.3632 × 10-5 J mol-1 K-4. For temperatures between 350 and 650 K the Cp can be described with the Debye equation using a constant Debye temperature of 996 K. For temperatures between 24 and 350 K the Debye temperature is a function of temperature and has a minimum value of 740 K at about 55 K. The Cp data for T 300 K were compared with those of AlN. As expected, the Cp data of MgSiN2 were about a factor 2 larger than those of AlN. The entropy ST, the enthalpy (HT - H0), and the energy function (GT - H0) in the range of 0-800 K were calculated using standard thermodynamic formulas. By extrapolating the Cp data to high temperatures at which GT is known, H0 was estimated to equal -534 kJ mol-1.

IntroductionMgSiN2 is a ternary adamantine type compound with tetrahedral coordination of Mg and Si. It can be deduced from the well-known AlN by systematically replacing two Al ions with one Mg and one Si ion. The properties of MgSiN2 ceramics have recently been reported.1 Because the thermal and mechanical properties of MgSiN2 ceramics look promising, we have started an investigation of the preparation, characterization, and properties of MgSiN2. This paper focuses in more detail on one thermal property, viz., the specific heat.

T (K) C p º (J mol-1 K-1) S T º (J mol-1 K-1)Cp/T

S T º (J mol-1 K-1)

0 0 0 0 0.000010 0.014 0.0045 0.0014 0.0047

20 0.109 0.0364 0.00545 0.0363

30 0.403 0.12 0.013433 0.1343

40 1.133 0.0325 0.028325 0.3379

50 2.367 0.701 0.04734 0.7227

60 4.088 1.275 0.068133 1.3004

70 6.206 2.062 0.088657 2.0774

80 8.593 3.046 0.107413 3.0480

90 11.154 4.206 0.123933 4.1992

100 13.912 5.521 0.13912 5.5129

110 16.65 6.975 0.151364 6.9692

120 19.484 8.545 0.162367 8.5478

130 22.337 10.217 0.171823 10.2293

140 25.183 11.977 0.179879 11.9963 m x6 m x5 m x4 m x3 m x2 m x b

150 28.001 13.811 0.186673 13.8338 9.16E-15 -9.91602E-12 4.24092E-09 -8.91636E-07 8.8164E-05 -0.00201299 0.016048 #N/A

160 30.774 15.707 0.192338 15.7292

170 33.488 17.654 0.196988 17.6723 T= 300 S= 44.55557513

180 36.135 19.644 0.20075 19.6551 T ref 20

190 38.708 21.667 0.203726 21.6709 S(20)= 0.036333333

200 41.201 23.716 0.206005 23.7143

210 43.612 25.785 0.207676 25.7803

220 45.938 27.868 0.208809 27.8640

230 48.181 29.959 0.209483 29.9602

240 50.34 32.056 0.20975 32.0631

250 52.416 34.153 0.209664 34.1669

260 54.41 36.248 0.209269 36.2655

270 56.325 38.338 0.208611 38.3542

280 58.161 40.42 0.207718 40.4301

290 59.921 42.491 0.206624 42.4946

300 61.713 44.551 0.20571 44.5556

Cp/T vs T

y = 9.16E-15x6 - 9.92E-12x5 + 4.24E-09x4 - 8.92E-07x3 + 8.82E-05x2 - 2.01E-03x + 1.60E-02R2 = 1.00E+00

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200 250 300

T/K

Cp

/Jm

ol-

1 K

-1

Entropía estándar

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300

T/K

Sº/

J m

ol-

1 K

-1