Properties of solids under the effect of high temperature and pressure- NaCI as an example
|
|
- Reynold Johnston
- 5 years ago
- Views:
Transcription
1 ndian Journal of Pure & Applied Physics Vol. 4, March 21, pp Properties of solids under the effect of high temperature and pressure- NaC as an example Munish Kumar Department of Physics, SRMS College of Engineering and Technology, Bareilly ( munish_dixit@yahoo.com) Received 5 September 2, accepted 22 December 2 A simple theoretical method is used to investigate the properties of solids nder varying conditions of temperature and pressure. The case of NaC is discussed as an example for the entire range of temperature and pressure, viz. from room temperature up to the melting temperature ( K) at the pressures varying from atmospheric pressure (referred as P = ) up to the structural transition pressure (P = 3 GPa). The results obtained for the temperature dependence of thermal expansivity are compared with those based on the widely used Suzuki equation. The results of the pressure dependence of thermal expansivity are compared with Anderson-Masuda rel ation. The results of Wang and Reeber [Phys Chem Miner, 23 (1996) 354] are also included for the sake of comparison. The good agreement with the avai lable theoretical as well as experimental data, supports the simple method used in the present paper. 1 ntroduction Kuswaha & Shanker 1 have compiled the methods reported by earlier workers for the determination of thermal expansivity. Such efforts may be used to study the isobaric (P = ) thermal expansion. Suzuki et at. 2 found what became known as the Suzuki equation, which yield the change in volume VV as a function of temperature T along the P = isobar. The detailed analysis of Suzuki equation is available elsewhere 2-4 and the mathematical form reads as follows: [ K - (1-4 KE Th Q ) 112 ] 2Ka... ( ) where K = (8' - 1)12 and Q = B V,[f. Bo, B'o are the isothermal bulk modulus and its first order pressure derivative, respectively, Yo is the Gruneisen ratio. The subscript refers to their value at P = and T = 3 K. ETh is the thermal energy, a equal to one, as discussed in detail by Anderson 3. Using the relation (YoETJV ) = PTh where PTh is the thermal pressure, Eq. () may be rewritten as follows: ~ - = - [ - { 2( B -1 ) B } p Th ] 12 V (B' -1)... (2) Eq. (2) may be used to determine isobaric (P = ) variation of VV versus T or the coefficient of volume thermal expansion a(7). The analytical expression for a(7) found by the differentiation of Eq. () is quite complicated. Therefore, the method of numerical differentiation has been suggested 3. Anderson 3 has discussed the limit of Suzuki equation for its applicability at high temperatures. t has been discussed 3 that it yields imaginary results for NaC at T > 736 K, and therefore not capable of explaining the thermal expansivity of NaC at P = isobar. Anderson & Masuda 5 have developed another method for the determination of a under the effect of pressure P. The formula reads as follows:... (3) where n = VV and ~~ is the value of a at n = for each isotherm. 8-r is the value of &rct) at high T and P =, K = 1.5. The application of Eq. (3) needs the input parameters measured along the temperature axis at P=O. Thus the problem becomes much difficult when one tries to investigate the properties of solids under the varying conditions of P and T. Thus, it is legitimate and may be useful to propose some simple method. n the present paper, an effort is made in this direction by developing a simple method. The method needs the values of input parameters at zero pressure and room temperature to
2 KUMAR: PROPERTES OF SOLDS 23 investigate the behaviour of solids under the varying conditions of pressure and temperature. NaC is a widely studied inorganic compound, because of its simple structure, high melting temperature and structural transition pressure. For this solid a large amount of theoretical as well as experimental data are available. The author has therefore selected NaC for the present study, so that the results may be discussed in the light of earlier studies. 2 Method of Analysis To investigate the properties of solids under varying conditions of pressure and temperature, the theory of equation of state recently developed by Kumar & Bedi 6 is extended. The detailed analysis is available elsewhere and the mathematical form reads as follows: l -=1--n V [ +-{P-a A B (T -T ) }...(4) V A B where P is the pressure, T the temperature and A = (8 T+ ), refers to the value at room temperature and atmospheric pressure. The coefficient of thermal expansion a is defined as a = (V)(dVdT)r. Therefore, from Eq. (4) one can get: a [ 1 AP, - = l--n{ Aa (T -T ) }f a A B { 1 + AP-Aa (T-Tr ) r' B o o -= B [ 1--n{l ArL(T-Tr)}] AP fii. A Bo --u o AP { 1+--An-(T -Tr)} B --u o... (5)... (6) The Anderson-Gruneisen parameter ~ is defined as: 8-1 (dbt J T-- abt dt )P Therefore, from Eq. (6) one can get: 3 Application Results and Discussion... (7) By making use of Eq. (4), the values of VV are investigated as a function of temperature along different isobars and reported in Fig.. The input data 3 are ~= 11.8 X o S K'' Bo = 24 GPa, 8 \ = 5.56 and 8 11 = Using the PTh values from Anderson, the values of VV at different T values are computed from Suzuki relation [Eq. (2)] at P = isobar. These results are reported in Fig. along with the results reported by Anderson 3, and Wang & ReeberR. Most of the results obtained are available up to 7 K. The author, therefore selected 7 K as a comparison point and data for VV are reported in Table. The results obtained in the present work are very close to the results reported by Anderson 3, and Wang & ReeberR. The results obtained by Suzuki formula are slightly low. At higher temperatures, the available data of Wang & ReeberR are used for comparison; a good agreement is obtained (Fig. 1). This demonstrates the effect of pressure on thermal expansion. t is found that thermal expansion is effected by pressure and it decreases as pressure is increased. Moreover, the isobar of P = 3 GPa is almost parallel to the temperature axis. This shows that at high pressure, the effect of temperature ts cancelled by the effect of pressure. Table -Comparison of VV at T = 7 K reported by earlier workers Reported by Anderson 3 Wang and ReeberR Suzuki Formula (Eq. 2) Present work (Eq. 4) VN The values of a calculated using Eq. (5) are reported in Figs 2 and 3 for the entire range of P and T. The results of a as a function of P and T reported by Wang & ReeberR are also given for the sake of comparison. The calculated values of a at P =, are found to lie between the two sets of the results reported by Wang & Reeber and Anderson 3 up to 6 K. Above 6 K, the calculated values of a are found to have a more rapid increase with the values of Wang & ReeberR, but this difference becomes very small as P is increased. This rapid increase of a with Tat P =, near melting temperature is
3 24 NDAN 1 PURE & APPL PHYS, VOL 4, MARCH 22 l.2.-- j~------~r ~ ~ ;e FP~-~D~GPa ~-Q ~ ~ P SGPa. 8 ~ ~ P - OGPa ~ ~P~Q~2GPa ~ FV3UGPa V/Vo Wang and Rceber 8.Andere on ' Suxull<1 for:rnula [ E q. C 21 ) - P resen t iudy Eq. ( 4 l ].2 t-- ol j L ~ ~------~L ~ _J Fig. -- Variation of V/V with temperature at diffe rent pressures ll ~ "-' 1j Wang and Reeber 8 -Present Study [Eq.(5)) P 1G Pa P"-2GPa * 25 ' 2... /.. ~ 15 ll... "-'1 d ',..., Wang and 3 Reebe r 8 + Anderson Suzilkf fomula [Bq,(l)J. - Present Study [Bq. ( 5)) P OGPa ~ * ~ * 2 * * * *' * * * * ~--~--~----L----~--~----~~ 3 ~ lf 9 1 Fig. 2 - Variati on of c1 with temperature consistent with theories of melting of alkali halides as di scussed in detai l by Shanker & Kumar 9 showing that a~ oo at T ~ TM. Anderson and Masuda have reported Eq. (3) for the determination of a as a function of T) along different isotherms. Making the use oft) values reported by Birch 1, ~~ (T) from Suzuki relation, and 8\ (T) from Anderson 3, the values of a are obtained along different isotherms using Eq. (3). The results thus ;j; 5 Fig. 3 - O. L----'-----'--~----"-- ~ ' Variation of a with temperatu re at diffe rent pressures obtained are reported in Fig. 4 along with those obtained using Eq. (5) reported in the present work. A good agreement is found. Here, it is pertinent to mention that the use of Anderson-Masuda relation [Eq. (3)] needs the values of rt along the isotherm considered and &r. a measured as a function of temperature at P =, as input data. On the other hand, Eq. (5) needs the input data at room temperature T = 3 K and P =. Thus, the application of Eq. (5) is simple as compared with Eq. (3).
4 KUMAR: PROPERTES OF SOLDS Anderson-Masuda rela tfon[eq ( 3) Jl. Present study [Eq.(5)] :: Ln ' P (GPa)! Fig. 4-Variation of a with pressure at different temperatures + lang and 3 Reeber 8 Anderson - Present study [Rq.(6)] 16 14r r ~p~ ~3~G~Pa t2 -.. ~ rll 6... P 2GPa Pa!OGPa. BOO 9 1 Fig. 5- Variation of bul k modulus with temperature at di fferent pressures The calculated values of bulk modulus as a function of T at different P using Eq. (6) are reported in Fig. 5. Anderson 3, Wang & ReeberR have 7 * P OGPa _.,_ 6it:=:Z=~=:j*t:::!*::~====~~ ~~~~~~a~ 5 Pt..5G!a ~ ~P~ OGPa.. 4 P 2GPa 2: Fig lang and 3 Reeber Anderson -Present Study [Hq.(7)] ~--~--L---~--~---L---L--~ T(K) Variation of &r with temperature at different pressures reported the variation of bulk modulus under the effect of temperature at P =. These results are al so included in Fig. 5 for the sake of compari son. A good agreement is obtained. The bulk modulus is found to decrease by increasing temperature and it
5 26 NDAN J PURE & APPL PHYS, VOL 4, MARCH 22 increases with increasing pressure. The decreasing behaviour of bulk n1odulus with increasing temperature is found to be less as the pressure increases. Al ong the hi ghest pressure isobar (P = 3 GPa) the percentage decrease the bulk modulus fro m 3 to K is found to be 4.58 %, which is very small as compared with the percentage decrease ( 48.8 % ), along P = isobar. Thus it seems that at hi gh temperatures, the effect of temperature is cancelled by the effect of pressure. The relati on investi gated fo r 8-r as a functi on of P and T [Eq. (7)] is used to predict the values of 8-r for the entire range of P and T. The results obtained are reported in Fi g. 6. The temperature dependence of 8T at P = is compared with the results reported by earl ier workersj.r. At most of the temperatures, the author's predicted values lie in between the two sets of resulth. 8-r is found to decrease by increasing pressure, which is consistent with the recent research in hi gh-pressure physics as di scussed in detail by Anderson 3 To summari se, the author has presented a simple method based on the knowledge of equation of state to in vesti gate the properties of solids under varying conditions of pressures and temperatures. A good agreement with the available theoretical as well as experimental data supports the validity of the simple method. The studies have been presented fo r the entire range of pressure and temperature even in the absence of experimental or theoretical data. Such an analys is may be useful fo r those engaged in the research at high pressures and high temperatures. References Kush wah S S & Shanker J, Phvsica 8, 225 ( 1996) Suzuki, Okaj ima S & Seya K, J Phys Earth, 27 ( 1979) Anderson L, Equation of state for geophysics and ceramic science (Oxford Un iversi ty Pr ss, Oxford), Anderson L, Mas uda K & Guo D, Phys Earth & Plane/a/)' n teriors, 89 ( 1995) Anderson L & Masuda K, Phys t -:arth & Planetary nteriors, 85 ( 1994) Kumar M & Bedi S S, Phys Status Solidi (b), 196 ( 1996) Kumar M, Physica 8, 2 12 ( 1995) 39 1; ( 1996) Wang K & Reeber R R, Phys Chem Miner, 23 ( 1996) Shanker J & Kumar M, Phys Status Solidi (b), 158 ( 199). Birch F, J Geophys Res, 9 1 ( 1986) 49.
Analysis of volume expansion data for periclase, lime, corundum and spinel at high temperatures
Bull. Mater. Sci., ol. 35, No., August, pp. 31 37. c Indian Academy of Sciences. Analysis of volume expansion data for periclase, lime, corundum and spinel at high temperatures BPSINGH, H CHANDRA, R SHYAM
More informationPressure Volume Temperature (P-V-T) Relationships and Thermo elastic Properties of Geophysical Minerals
Pressure Volume Temperature (P-V-T) Relationships and Thermo elastic Properties of Geophysical Minerals A PROPOSAL FOR Ph.D PROGRAMME BY MONIKA PANWAR UNDER THE SUPERVISION OF DR SANJAY PANWAR ASSISTANT
More informationVolume Thermal Expansion for Ionic Solids at High Temperatures
International Journal of Engineering and Mathematical Sciences Jan.- June 1, olume 1, Issue -1, pp.7- ISSN (rint) 19-457, (Online) 19-4545. All rights reserved (www.ijems.org) IJEMS olume hermal Expansion
More informationCanadian Journal of Physics. Higher Order derivatives of bulk modulus of materials at infinite pressure
Higher Order derivatives of bulk modulus of materials at infinite pressure Journal: Manuscript ID cjp-015-0699.r Manuscript Type: Article Date Submitted by the Author: 0-Apr-016 Complete List of Authors:
More informationEvaluation of pressure and bulk modulus for alkali halides under high pressure and temperature using different EOS
Journal of the Association of Arab Uniersities for Basic and Applied Sciences (3) 4, 38 45 Uniersity of Bahrain Journal of the Association of Arab Uniersities for Basic and Applied Sciences www.elseier.com/locate/jaaubas
More informationTemperature dependent study of volume and thermal expansivity of solids based on equation of state
Indian Journal of Pure & Applied Physics ol. 47, August 009, pp. 59-596 emperature dependent study of volume and ermal expansivity of solids based on equation of state Kamal Kapoor & Narsingh Dass Physics
More informationEMPORIUM H O W I T W O R K S F I R S T T H I N G S F I R S T, Y O U N E E D T O R E G I S T E R.
H O W I T W O R K S F I R S T T H I N G S F I R S T, Y O U N E E D T O R E G I S T E R I n o r d e r t o b u y a n y i t e m s, y o u w i l l n e e d t o r e g i s t e r o n t h e s i t e. T h i s i s
More informationEOS-FIT V6.0 R.J. ANGEL
EOS-FIT V6. R.J. AGEL Crystallography Laboratory, Dept. Geological Sciences, Virginia Tech, Blacksburg, VA46, USA http://www.geol.vt.edu/profs/rja/ ITRODUCTIO EosFit started as a program to fit equations
More informationImpact of size and temperature on thermal expansion of nanomaterials
PRAMANA c Indian Academy of Sciences Vol. 84, No. 4 journal of April 205 physics pp. 609 69 Impact of size and temperature on thermal expansion of nanomaterials MADAN SINGH, and MAHIPAL SINGH 2 Department
More informationMelting Temperature of Lithium, Sodium and Potassium at High Pressures
International Journal of Applied Science and Technology Vol. No. 4; April 1 Melting Teperature of Lithiu, Sodiu and Potassiu at High Pressures Chuanhui Nie Shangyong Huang Wei Huang School of Science,
More informationNEW RELATION BETWEEN VOLUME THERMAL EXPANSION AND THERMAL PRESSURE FOR SOLIDS
NEW RELATION BETWEEN VOLUME THERMAL EXANSION AND THERMAL RESSURE FOR SOLIDS Sumiti Narayan Tewari 1, Anita Shukla 1, Department of hysics, ranveer Singh Institute of Technology, Bhauti, Kanpur 8 U.. (India)
More informationPressure derivatives of bulk modulus for materials at extreme compression
Indian Journal o ure & Applied hysics Vol. 5, October, pp. 734-738 ressure derivatives o bulk modulus or materials at extreme compression Singh* & A Dwivedi Department o hysics, Institute o Basic Sciences,
More informationCOMPARATIVE ANALYSIS OF THERMO-ELASTIC PROPERTIES OF ZINC OXIDE NANOMATERIALS AT HIGH TEMPERATURES
http:// COMPARATIVE ANALYSIS OF THERMO-ELASTIC PROPERTIES OF ZINC OXIDE NANOMATERIALS AT HIGH TEMPERATURES Krishna Chandra 1, Mahipal Singh2, Luv Kush3 and Madan Singh4 1,2,3 Department of Physics, R.H.
More informationAmerican International Journal of Research in Formal, Applied & Natural Sciences
American International Journal of Research in Formal, Applied & Natural Sciences Available online at http://www.iasir.net ISSN (Print): 2328-3777, ISSN (Online): 2328-3785, ISSN (CD-ROM): 2328-3793 AIJRFANS
More informationEstimation of diffusion coefficients of Cr 3+ Ga 3+ in MgO at temperatures of the Earth s lower mantle.
International Journal of Scientific & Engineering Research Volume 4, Issue 1, January-2013 1 Estimation of diffusion coefficients of Cr 3+ Ga 3+ in MgO at temperatures of the Earth s lower mantle. and
More informationMelting of Li, K, Rb and Cs at high pressure
Melting of Li, K, Rb and Cs at high pressure R N Singh and S Arafin Abstract Lindemann s melting law has been used to develop analytical expression to determine the pressure (P) dependence of the melting
More informationPressure Volume Temperature Equation of State
Pressure Volume Temperature Equation of State S.-H. Dan Shim ( ) Acknowledgement: NSF-CSEDI, NSF-FESD, NSF-EAR, NASA-NExSS, Keck Equations relating state variables (pressure, temperature, volume, or energy).
More informationThermophysical Properties from the Equation of State of Mason and Co-workers ~
hlternational Journal of Tlwrmophysic.~ ~. I.'ol. IA', No. 4. 1997 Thermophysical Properties from the Equation of State of Mason and Co-workers ~ A. Boushehri 2" 3 and H. Eslami 2 The theory gives formuhts
More informationThermodynamical properties of neutron matter using Gogny effective interaction
Indian Journal of Pure & Applied Physics Vol. 4 1, September 2003, pp. 675-680 Thermodynamical properties of neutron matter using Gogny effective interaction Kh A Ramadan & H M M Mansour Physics Department,
More informationFrequency and Composition Dependence on the Dielectric Properties for Mg-Zn Ferrite.
Egypt. J. Solids, Vol. (28), No. (2), (2005) 263 Frequency and Composition Dependence on the Dielectric Properties for Mg-Zn Ferrite. S. F. Mansour Zagazig University, Faculty of Science, Physics Department
More informationHigher Order Elastic Constants of Thorium Monochalcogenides
Bulg. J. Phys. 37 (2010) 115 122 Higher Order Elastic Constants of Thorium Monochalcogenides K.M. Raju Department of Physics, Brahmanand P.G. College, Rath (Hamirpur), Uttar Pradesh, 210 431, India Received
More informationThe calculation of ternary miscibility gaps using the linear contributions method: Problems, benchmark systems and an application to (K, Li, Na)Br
Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 185 190 www.elsevier.com/locate/calphad The calculation of ternary miscibility gaps using the linear contributions method: Problems, benchmark
More informationThermodynamic Functions at Isobaric Process of van der Waals Gases
Thermodynamic Functions at Isobaric Process of van der Waals Gases Akira Matsumoto Department of Material Sciences, College of Integrated Arts Sciences, Osaka Prefecture University, Sakai, Osaka, 599-853,
More informationTwo Universal Equations of State for Solids
Two Universal Equations of State for Solids Jiu-Xun Sun a,b,qiangwu b,yangguo a, and Ling-Cang Cai b a Department of Applied Physics, University of Electronic Science and Technology, Chengdu 610054, China
More informationCORRELATION BETWEEN STANDARD ENTHALPY OF FORMATION AND REFRACTIVE INDEX IN ALKALI HALIDES
Int. J. Chem. Sci.: 7(4), 2009, 2489-2494 CORRELATION BETWEEN STANDARD ENTHALPY OF FORMATION AND REFRACTIVE INDEX IN ALKALI HALIDES A. NASAR * P. G. Department of Chemistry, Shibli National College, AZAMGARH
More informationPhysical Chemistry I CHEM 4641 Final Exam 13 questions, 30 points
Physical Chemistry I CHEM 4641 Final Exam 13 questions, 30 points Name: KEY Gas constant: R = 8.314 J mol -1 K -1 = 0.008314 kj mol -1 K -1. Boltzmann constant k = 1.381 10-23 J/K = 0.6950 cm -1 /K h =
More informationFURTHER MEYER-NELDEL RULE IN a-se 70 Te 30-x Zn x THIN FILMS
Journal of Ovonic Research Vol. 5, No. 5, October 009, p. 15-1 FURTHER MEYER-NELDEL RULE IN a-se 70 Te 0-x Zn x THIN FILMS R. K. PAL, A. K. AGNIHOTRI, P. K. DWIVEDI a, A. KUMAR b* Physics Department, B.
More informationP a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
More informationTHERMOPHYSICAL PROPERTIES OF THORIUM COMPOUNDS FROM FIRST PRINCIPLES
THERMOPHYSICAL PROPERTIES OF THORIUM COMPOUNDS FROM FIRST PRINCIPLES Vinayak Mishra a,* and Shashank Chaturvedi a a Computational Analysis Division, Bhabha Atomic Research Centre, Visakhapatnam 530012,
More information176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
More informationHardness Prediction and First Principle Study of Re-123(Re = Y, Eu, Pr, Gd) Superconductors
316 Bull. Korean Chem. Soc. 29, Vol. 3, No. 12 Weiwei Liu et al. DOI 1.512/bkcs.29.3.12.316 Hardness Prediction and First Principle Study of Re-123(Re = Y, Eu, Pr, Gd Superconductors Weiwei Liu,, Y. P.
More information1 What is a differential equation
Math 10B - Calculus by Hughes-Hallett, et al. Chapter 11 - Differential Equations Prepared by Jason Gaddis 1 What is a differential equation Remark 1.1. We have seen basic differential equations already
More informationTemperature and pressure dependence of the Raman frequency shifts in anthracene
Indian Journal of Pure & Applied Physics Vol. 54, August 2016, pp. 489-494 Temperature and pressure dependence of the Raman frequency shifts in anthracene H Özdemir & H Yurtseven* Department of Physics,
More informationA simple model for calculating the bulk modulus of the mixed ionic crystal: NH 4 Cl 1 x Br x
PRAMANA c Indian Academy of Sciences Vol. 77, No. 4 journal of October 2011 physics pp. 689 695 A simple model for calculating the bulk modulus of the mixed ionic crystal: NH 4 Cl 1 x Br x VASSILIKI KATSIKA-TSIGOURAKOU
More informationSeismic velocity decrement ratios for regions of partial melt near the core-mantle boundary
Stanford Exploration Project, Report 02, October 25, 999, pages 87 20 Seismic velocity decrement ratios for regions of partial melt near the core-mantle boundary James G. Berryman keywords: poroelasticity,
More informationScholars Research Library
Available online at www.scholarsresearchlibrary.com Archives of Physics Research, 2015, 6 (5):5-10 (http://scholarsresearchlibrary.com/archive.html) ISSN : 0976-0970 CODEN (USA): APRRC7 The determination
More informationAn ion-aerosol model study for the stratospheric conductivity under enhanced aerosol condition
Indian Journal of Radio & Space Physics Vol., February 2001, pp. 31-35 An ion-aerosol model study for the stratospheric conductivity under enhanced aerosol condition N Srinivas, B S N Prasad & K Nagaraja
More informationA L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
More informationUNCLASSIFIED Reptoduced. if ike ARMED SERVICES TECHNICAL INFORMATION AGENCY ARLINGTON HALL STATION ARLINGTON 12, VIRGINIA UNCLASSIFIED
. UNCLASSIFIED. 273207 Reptoduced if ike ARMED SERVICES TECHNICAL INFORMATION AGENCY ARLINGTON HALL STATION ARLINGTON 12, VIRGINIA UNCLASSIFIED NOTICE: When government or other drawings, specifications
More informationFree Convective Heat Transfer From A Vertical Surface For The Case Of Linearly Varying Thermal Potential
American Journal of Engineering Research (AJER) e-issn : 232-847 p-issn : 232-936 Volume-2, Issue-9, pp-71-75 www.ajer.org Research Paper Open Access Free Convective Heat Transfer From A Vertical Surface
More informationBCIT Fall Chem Exam #2
BCIT Fall 2017 Chem 3310 Exam #2 Name: Attempt all questions in this exam. Read each question carefully and give a complete answer in the space provided. Part marks given for wrong answers with partially
More informationTHIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.
T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson
More informationAb initio Predictions of Structural and Thermodynamic Properties of Zr 2 AlC Under High Pressure and High Temperature
CHINESE JOURNAL OF CHEMICAL PHYSICS VOLUME 28, NUMBER 3 JUNE 27, 215 ARTICLE Ab initio Predictions of Structural and Thermodynamic Properties of Zr 2 AlC Under High Pressure and High Temperature Fen Luo
More informationVolume dependence of the Grüneisen ratio for shock-wave equation-of-state studies
Volume dependence of the Grüneisen ratio for shock-wave equation-of-state studies arxiv:140041v1 [cond-mat.mtrl-sci] 6 Jan 014 Valentin Gospodinov Space Research and Technology Institute BAS BG-1000, Sofia,
More informationMean spherical model-structure of liquid argon
Prami0a, Vol. 6, No 5, 1976, pp. 284-290. Printed in ndia. Mean spherical model-structure of liquid argon R V GOPALA RAO and T NAMMALVAR Department of Physical Chemistry, Jadavpur University, Calcutta
More informationPeculiarities of first-order phase transitions in the presence of an electric field
Peculiarities of first-order phase transitions in the presence of an electric field Yu. Dolinsky* and T. Elperin The Pearlstone Center for Aeronautical Engineering Studies Department of Mechanical Engineering
More informationThe first law of thermodynamics continued
Lecture 7 The first law of thermodynamics continued Pre-reading: 19.5 Where we are The pressure p, volume V, and temperature T are related by an equation of state. For an ideal gas, pv = nrt = NkT For
More informationPressure-dependent viscosity and free volume of activation in hydrocarbons and other liquids
International Journal of ChemTech Research CODEN (USA): IJCRGG ISSN : 0974-4290 Vol.6, No.14, pp 5503-5509, Nov-Dec 2014 Pressure-dependent viscosity and free volume of activation in hydrocarbons and other
More informationT h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
More informationPorosity dependence of Elastic Modulii for Ceramic Materials
ISSN 394 3386 Volume 4, Issue 1 December 017 Porosity dependence of Elastic Modulii for Ceramic Materials R. K. Sharma a *, A.K.Upadhyay b & S. B. Sharma c a Department of Physics, B.S.A. College of Engg.
More informationMechanisms inherent in the thermoluminescence processes
Indian Journal of Pure & Applied Physics Vol. 42, August 2004, pp 565-571 Mechanisms inherent in the thermoluminescence processes J Prakash, S K Rai, P K Singh & H O Gupta Department of Physics, D D U
More informationSpeeds of sound and isothermal compressibility of ternary liquid systems: Application of Flory s statistical theory and hard sphere models
PRAMANA c Indian Academy of Sciences Vol. 70, No. 4 journal of April 2008 physics pp. 731 738 Speeds of sound and isothermal compressibility of ternary liquid systems: Application of Flory s statistical
More informationOH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
More informationPhysics 141. Lecture 24.
Physics 141. Lecture 24. 0.5 µm particles in water, 50/50 glycerol-water, 75/25 glycerol-water, glycerol http://www.physics.emory.edu/~weeks/squishy/brownianmotionlab.html Frank L. H. Wolfs Department
More informationThermodynamics of Three-phase Equilibrium in Lennard Jones System with a Simplified Equation of State
23 Bulletin of Research Center for Computing and Multimedia Studies, Hosei University, 28 (2014) Thermodynamics of Three-phase Equilibrium in Lennard Jones System with a Simplified Equation of State Yosuke
More informationW2 = N (I + Pp + Qp2)
Physics. - Measurements about the velocity of sound in hydrogen gas at liquid hydrogen temperatures. By A. VAN TTERBE EK and W. H. KEESOM. (Communication N0. 216c from the Physical Laboratory at Leiden).
More informationEnergy: 1. Energy is an abstract physical quantity 2. It can be measured only by means of its effect Vikasana - Bridge Course
BASICS OF THERMODYNAMICS Vikasana - Bridge Course 2012 1 Energy: 1. Energy is an abstract physical quantity 2. It can be measured only by means of its effect Vikasana - Bridge Course 2012 2 HEAT Heat is
More informationStrong light matter coupling in two-dimensional atomic crystals
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHOTON.2014.304 Strong light matter coupling in two-dimensional atomic crystals Xiaoze Liu 1, 2, Tal Galfsky 1, 2, Zheng Sun 1, 2, Fengnian Xia 3, Erh-chen Lin 4,
More informationChapter 8 Phase Diagram, Relative Stability of Solid, Liquid, and Gas
Chapter 8 Phase Diagram, Relative Stability of Solid, Liquid, and Gas Three states of matter: solid, liquid, gas (plasma) At low T: Solid is most stable. At high T: liquid or gas is most stable. Ex: Most
More informationThermal dehydration and degradation kinetics of chitosan Schiff bases of o- and m nitrobenzaldehyde Muraleedharan K.* & Viswalekshmi C.H.
2017 St. Joseph s College (Autonomous), Devagiri www.devagirijournals.com ISSN 2454-2091 Thermal dehydration and degradation kinetics of chitosan Schiff bases of o- and m nitrobenzaldehyde Muraleedharan
More informationDepartment of Physics, Anna University, Sardar Patel Road, Guindy, Chennai -25, India.
Advanced Materials Research Online: 2013-02-13 ISSN: 1662-8985, Vol. 665, pp 43-48 doi:10.4028/www.scientific.net/amr.665.43 2013 Trans Tech Publications, Switzerland Electronic Structure and Ground State
More informationdg = V dp - S dt (1.1) 2) There are two T ds equations that are useful in the analysis of thermodynamic systems. The first of these
CHM 3410 Problem Set 5 Due date: Wednesday, October 7 th Do all of the following problems. Show your work. "Entropy never sleeps." - Anonymous 1) Starting with the relationship dg = V dp - S dt (1.1) derive
More informationIMPROVEMENT OF AN APPROXIMATE SET OF LATENT ROOTS AND MODAL COLUMNS OF A MATRIX BY METHODS AKIN TO THOSE OF CLASSICAL PERTURBATION THEORY
IMPROVEMENT OF AN APPROXIMATE SET OF LATENT ROOTS AND MODAL COLUMNS OF A MATRIX BY METHODS AKIN TO THOSE OF CLASSICAL PERTURBATION THEORY By H. A. JAHN {University of Birmingham) [Received 7 October 947]
More informationPhysics 141. Lecture 24. December 5 th. An important day in the Netherlands. Physics 141. Lecture 24. Course Information. Quiz
Physics 141. Lecture 24. 0.5 µm particles in water, 50/50 glycerol-water, 75/25 glycerol-water, glycerol http://www.physics.emory.edu/~weeks/squishy/brownianmotionlab.html Frank L. H. Wolfs Department
More information1. NMR Spectrum of the prepared energetic salts. Figure S1. 1 H NMR spectrum of diammonium BNOA (6)
Electronic Supplementary Material (ESI) for Dalton Transactions. This journal is The Royal Society of Chemistry 2016 1. MR Spectrum of the prepared energetic salts Figure S1. 1 H MR spectrum of diammonium
More informationB.K. Singh et al./ BIBECHANA 14 (2017) : RCOST p.16 (Online Publication: Dec., 2016)
B.K. Singh et al./ BIBECHANA 14 (2017) 16-29 : RCOST p.16 (Online Publication: Dec., 2016) BIBECHANA A Multidisciplinary Journal of Science, Technology and Mathematics ISSN 2091-0762 (Print), 2382-5340
More informationProperties of calcium fluoride up to 95 kbar: A theoretical study
Bull. Mater. Sci., Vol. 33, No. 4, August 2010, pp. 413 418. Indian Academy of Sciences. Properties of calcium fluoride up to 95 kbar: A theoretical study CHUN-SHENG WANG School of Traffic and Transportation,
More informationUnified analyses for P-V-T equation of state of MgO: A solution for pressure-scale problems in high P-T experiments
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi:10.1029/2008jb005813, 2009 Unified analyses for P-V-T equation of state of MgO: A solution for pressure-scale problems in high P-T experiments Yoshinori
More informationEquations of State. Tiziana Boffa Ballaran
Equations o State iziana Boa Ballaran Why EoS? he Earth s interior is divided globally into layers having distinct seismic properties Speed with which body waves travel through the Earth s interior are
More informationDepartment of Physics, Kyoto University Kyoto
29 Progress of Theoretical Physics, Vol. :12, No. 1, July 1964 Pauli Para.mag:netism and Superconducting State. II Kazumi MAKI*) Department of Physics, Kyoto University Kyoto (Received March 11, 1964)
More informationLATTICE DYNAMICS OF METALLIC GLASS M.M. SHUKLA
Vol. 94 (1998) ACTA PHYSICA POLONICA A No. 4 LATTICE DYNAMICS OF METALLIC GLASS Ca70 Μg30 ON THE MODEL OF BHATIA AND SINGH M.M. SHUKLA Departamento de Fisica, UNESP, Bauru, C.P. 473, 17033-360, Bauru,
More informationOCN 623: Thermodynamic Laws & Gibbs Free Energy. or how to predict chemical reactions without doing experiments
OCN 623: Thermodynamic Laws & Gibbs Free Energy or how to predict chemical reactions without doing experiments Definitions Extensive properties Depend on the amount of material e.g. # of moles, mass or
More informationUsing the Entropy Rate Balance to Determine the Heat Transfer and Work in an Internally Reversible, Polytropic, Steady State Flow Process
Undergraduate Journal of Mathematical Modeling: One + Two Volume 8 08 Spring 08 Issue Article Using the Entropy Rate Balance to Determine the Heat Transfer and Work in an Internally Reversible, Polytropic,
More informationPHY214 Thermal & Kinetic Physics Duration: 2 hours 30 minutes
BSc Examination by course unit. Friday 5th May 01 10:00 1:30 PHY14 Thermal & Kinetic Physics Duration: hours 30 minutes YOU ARE NOT PERMITTED TO READ THE CONTENTS OF THIS QUESTION PAPER UNTIL INSTRUCTED
More informationData for Titan, a moon of Saturn, is given below, and may be used to answer problems 1 and 2.
CHM 5423 Atmospheric Chemistry Problem Set 1 Due date: Thursday, September 10 th. Do the following problems. Show your work. Data for Titan, a moon of Saturn, is given below, and may be used to answer
More informationE21-3 (a) We ll assume that the new temperature scale is related to the Celsius scale by a linear. T S = mt C + b, (0) = m( C) + b.
E1-1 (a) We ll assume that the new temperature scale is related to the Celsius scale by a linear transformation; then T S = mt C + b, where m and b are constants to be determined, T S is the temperature
More informationIntroduction into thermodynamics
Introduction into thermodynamics Solid-state thermodynamics, J. Majzlan Chemical thermodynamics deals with reactions between substances and species. Mechanical thermodynamics, on the other hand, works
More informationTheoretical explanation of the uniform compressibility behavior observed in oxide spinels
PHYSICAL REVIEW B, VOLUME 6, 184101 heoretical explanation of the uniform compressibility behavior observed in oxide spinels J. M. Recio, R. Franco, A. Martín Pendás, M. A. Blanco, and L. Pueyo Departamento
More informationTemperature effect on lyoluminescence of potassium halide microcrystals in luminol solution
Indian Journal of Pure & Applied Physics Vol. 44, July 2006, pp. 519-523 Temperature effect on lyoluminescence of potassium halide microcrystals in luminol solution R S Chandok*, R Kaur**, G K Chandok
More informationRaman Studies on Functional Perovskite Oxides
Raman Studies on Functional Perovskite Oxides Venkata S. Bhadram Postdoctoral Research Associate Geophysical Laboratory Carnegie Institution for Science Bangalore Jawaharlal Nehru Centre for Advanced Scientific
More informationPROCEEDINGS SECOND WORKSHOP GEOTHERMAL RESERVOIR ENGINEERING December 1-3,
-- --- -- - -------- ---- - -- -- ------- -- - -- ---- SGP-TR-2-34 PROCEEDNGS SECOND WORKSHOP GEOTHERMAL RESERVOR ENGNEERNG December -3,976 976 'Conducted under Grant No. NSF-AER-72-349 supported by the
More informationMeasurement of atomic number and mass attenuation coefficient in magnesium ferrite
PRAMANA c Indian Academy of Sciences Vol. 68, No. 5 journal of May 2007 physics pp. 869 874 Measurement of atomic number and mass attenuation coefficient in magnesium ferrite R H KADAM 1,STALONE 2,GKBICHILE
More informationProblem Set 9 Solutions. (a) Using the guess that the value function for this problem depends only on y t and not ε t and takes the specific form
EC 720 - Math for Economists Samson Alva Department of Economics, Boston College December 9, 20 roblem Set 9 Solutions. Stochastic Linear-Quadratic Dnamic rogramming (a) Using the guess that the value
More informationDielectric studies and microwave emissivity of alkaline soil of Alwar with mixing of gypsum
Material Science Research India Vol. 7(2), 519-524 (2010) Dielectric studies and microwave emissivity of alkaline soil of Alwar with mixing of gypsum V.K. GUPTA*, R.A. JANGID and SEEMA YADAV Microwave
More informationOn the local and nonlocal components of solvation thermodynamics and their relation to solvation shell models
JOURNAL OF CHEMICAL PHYSICS VOLUME 109, NUMBER 12 22 SEPTEMBER 1998 On the local and nonlocal components of solvation thermodynamics and their relation to solvation shell models Nobuyuki Matubayasi Institute
More informationWeek 1 Temperature, Heat and the First Law of Thermodynamics. (Ch. 19 of Serway&J.)
Week 1 Temperature, Heat and the First Law of Thermodynamics. (Ch. 19 of Serway&J.) (Syllabus) Temperature Thermal Expansion Temperature and Heat Heat and Work The first Law Heat Transfer Temperature Thermodynamics:
More informationThermal equation of state of (Mg 0.9 Fe 0.1 ) 2 SiO 4 olivine
Physics of the Earth and Planetary Interiors 157 (2006) 188 195 Thermal equation of state of (Mg 0.9 Fe 0.1 ) 2 SiO 4 olivine Wei Liu, Baosheng Li Mineral Physics Institute, Stony Brook University, Stony
More informationI-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. l"l. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S l"l. \ (?
>. 1! = * l >'r : ^, : - fr). ;1,!/!i ;(?= f: r*. fl J :!= J; J- >. Vf i - ) CJ ) ṯ,- ( r k : ( l i ( l 9 ) ( ;l fr i) rf,? l i =r, [l CB i.l.!.) -i l.l l.!. * (.1 (..i -.1.! r ).!,l l.r l ( i b i i '9,
More informationNAME: NITROMETHANE CHEMISTRY 443, Fall, 2015(15F) Section Number: 10 Final Examination, December 18, 2015
NAME: NITROMETHANE CHEMISTRY 443, Fall, 015(15F) Section Number: 10 Final Examination, December 18, 015 Answer each question in the space provided; use back of page if extra space is needed. Answer questions
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Chemistry 5.76 Revised February, 1982 NOTES ON MATRIX METHODS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Chemistry 5.76 Revised February, 198 NOTES ON MATRIX METHODS 1. Matrix Algebra Margenau and Murphy, The Mathematics of Physics and Chemistry, Chapter 10, give almost
More informationANALYTIC SOLUTIONS OF A FUNCTIONAL DIFFERENTIAL EQUATION WITH STATE DEPENDENT ARGUMENT. Jian-Guo Si and Sui Sun Cheng
TWIWANESE JOURNAL OF MATHEMATICS Vol., No. 4, pp. 47-480, December 997 ANALYTIC SOLUTIONS OF A FUNCTIONAL DIFFERENTIAL EQUATION WITH STATE DEPENDENT ARGUMENT Jian-Guo Si and Sui Sun Cheng Abstract. This
More informationDonald G. Isaak. University of Redlands Physics B.Sc., 1973 Pennsylvania State University Geophysics M.Sc., 1975 UCLA Geophysics Ph.D.
Donald G. Isaak Executive Director Office of Research and Grants Azusa Pacific University Azusa, California 91702-7000 phone: (626) 815-6000 (ext. 3796) email: disaak@apu.edu Education University of Redlands
More informationThe efficiency at maximum power output of endoreversible engines under combined heat transfer modes
The efficiency at maximum power output of endoreversible engines under combined heat transfer modes F. MOUKALLED, Faculty of Engineering and Architecture, Mechanical Engineering Department, American University
More informationThe temperature dependence of the isothermal bulk modulus at 1 bar pressure
he temerature deendence of the isothermal bulk modulus at bar ressure J. Garai a) Det. of Earth Sciences, Florida International University, University Park, PC 344, Miami, FL 3399, USA A. Laugier IdPCES
More informationTHE AMERICAN MINERALOGIST, VOL.51, MAY-JUNE. 1966
THE AMERICAN MINERALOGIST, VOL.51, MAY-JUNE. 1966 COMPOSITIONAL VARIATIONS OF PLAGIOCLASE FELDSPAR FROM A BASALTIC LAVA FLOW Jnnnv M. Honlnn, Department of Geology, Teras Western College, El Paso, Teras.
More information2/23/2018. Familiar Kinetics. ...and the not so familiar. Chemical kinetics is the study of how fast reactions take place.
CHEMICAL KINETICS & REACTION MECHANISMS Readings, Examples & Problems Petrucci, et al., th ed. Chapter 20 Petrucci, et al., 0 th ed. Chapter 4 Familiar Kinetics...and the not so familiar Reaction Rates
More informationPhase Changes and Latent Heat
Review Questions Why can a person remove a piece of dry aluminum foil from a hot oven with bare fingers without getting burned, yet will be burned doing so if the foil is wet. Equal quantities of alcohol
More informationFIRST PRINCIPLES STUDY OF AlBi
Available at: http://publications.ictp.it IC/2008/025 United Nations Educational, Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL
More informationPrediction of Elastic Constants on 3D Four-directional Braided
Prediction of Elastic Constants on 3D Four-directional Braided Composites Prediction of Elastic Constants on 3D Four-directional Braided Composites Liang Dao Zhou 1,2,* and Zhuo Zhuang 1 1 School of Aerospace,
More informationChapter 6. Heat capacity, enthalpy, & entropy
Chapter 6 Heat capacity, enthalpy, & entropy 1 6.1 Introduction In this lecture, we examine the heat capacity as a function of temperature, compute the enthalpy, entropy, and Gibbs free energy, as functions
More information