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Mohan Sai Kiran Kumar Yadav Nartu, Shashank Sharma, Srinivas Aditya Mantri, Sameehan S. Joshi, Mangesh V. Pantawane ...
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Clausius-Clapeyron equation
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Search Results for Clausius-Clapeyron equation
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Book Chapter
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005448
EISBN: 978-1-62708-196-2
... for a particular fluid. The Clausius equation of state is expressed as: p ( ∀ − b ′ ) = m R T where: b ′ = 16 3 N π r 3 r = one-half the center-to-center distance of two colliding molecules N = number of molecules in volume V The Redlich-Kwong...
Abstract
This article is a comprehensive collection of the thermodynamic equations and property relations of the first and second laws of thermodynamics that are applicable to closed-system consisting of several homogeneous and heterogeneous phases.
Book Chapter
Book: Alloy Phase Diagrams
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006221
EISBN: 978-1-62708-163-4
.... age hardening allotropy alloying aluminum-copper system binary system Clausius-Clapeyron equation crystal structure Gibbs phase rule heat treatment iron-carbon phase diagram Lever rule phase diagram polymorphism solid-state transformation solidification ternary diagrams Theorem of Le...
Abstract
The application of phase diagrams is instrumental in solid-state transformations for the processing and heat treatment of alloys. A unary phase diagram plots the phase changes of one element as a function of temperature and pressure. This article discusses the unary system that can exist as a solid, liquid, and/or gas, depending on the specific combination of temperature and pressure. It describes the accomplishment of conversion between weight percentage and atomic percentage in a binary system by the use of formulas. The article analyzes the effects of alloying on melting/solidification and on solid-state transformations. It explains the construction of phase diagrams by the Gibbs phase rule and the Lever rule. The article also reviews the various types of alloy systems that involve solid-state transformations. It concludes with information on the sources of phase diagram.
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003085
EISBN: 978-1-62708-199-3
....) Clausius-Clapeyron Equation The theorem of Le Châtelier was quantified by Benoit Clapeyron and Rudolf Clausius to give the following equation: d P d T = Δ H t Δ V where dP/dT is the slope of the univariant lines in a PT diagram such as those shown in Fig. 2 , Δ V...
Abstract
Alloy phase diagrams are useful for the development, fabrication, design and control of heat treatment procedures that will produce the required mechanical, physical, and chemical properties of new alloys. They are also useful in solving problems that arise in their performance in commercial applications, thus improving product predictability. This article describes different equilibrium phase diagrams (unary, binary, and ternary) and microstructures, description terms, and general principles of reading alloy phase diagrams. Further, the article discusses plotting schemes; areas in a phase diagram; and the position and shapes of the points, lines, surfaces, and intersections, which are controlled by thermodynamic principles and properties of all phases that comprise the system. It also illustrates the application of the stated principles with suitable phase diagrams.
Series: ASM Handbook
Volume: 23
Publisher: ASM International
Published: 01 June 2012
DOI: 10.31399/asm.hb.v23.a0005658
EISBN: 978-1-62708-198-6
...-induce martensite as well as thermally induce martensite. The relationship between temperature and stress in governing the transformation is given by the Clausius-Clapeyron equation: (Eq 1) d σ / d T = Δ H / ε t T o where σ is the applied stress, Δ H is the latent heat...
Abstract
This article focuses on the specific aspects of nitinol that are of interest to medical device designers. It describes the physical metallurgy, physical properties, and tensile properties of the nitinol. The article discusses the factors influencing superelastic shape memory effects, fatigue, and corrosion in medical device design. It reviews the biocompatibility of nitinol based on corrosion behavior. The article explains the general principles, potential pitfalls, and key properties for manufacturing, heat treatment, and processing of nitinol.
Book Chapter
Book: Alloy Phase Diagrams
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006223
EISBN: 978-1-62708-163-4
... As a result, Eq 16 becomes: (Eq 17) ( d P d T ) eq = Δ H T Δ V which is one form of the Clausius-Clapeyron equation. Because close-packed γ iron has a smaller molar volume than α-iron, Δ V = V mβ − V mα < 0, while Δ H = H γ − H α < 0...
Abstract
Thermodynamic descriptions have become available for a large number of alloy systems and allow the calculation of the phase diagrams of multicomponent alloys. This article begins with a discussion on three laws of thermodynamics: the Law of Conservation of Energy, the Second Law of Thermodynamics, and the Third Law of Thermodynamics. It informs that for transformations that occur at a constant temperature and pressure, the relative stability of the system is determined by its Gibbs free energy. The article describes the Gibbs free energy of a single-component unary system and the Gibbs free energy of a binary solution. It schematically illustrates the structure of a binary solid solution with interatomic bonds and shows how the equilibrium state of an alloy can be obtained from the free-energy curves at a given temperature. The article concludes with information on the construction of eutectic and binary phase diagrams from Gibbs free-energy curves.
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005636
EISBN: 978-1-62708-174-0
... welding. The article presents the mathematical equations of mass, momentum, energy, and species conservation. It reviews the applications of heat transfer and fluid flow models for different welding processes. Finally, the article discusses the approaches to improve reliability of, and reduce uncertainty...
Abstract
This article provides a comprehensive review and critical assessment of numerical modeling of heat and mass transfer in fusion welding. The different fusion welding processes are gas tungsten arc welding, gas metal arc welding, laser welding, electron beam welding, and laser-arc hybrid welding. The article presents the mathematical equations of mass, momentum, energy, and species conservation. It reviews the applications of heat transfer and fluid flow models for different welding processes. Finally, the article discusses the approaches to improve reliability of, and reduce uncertainty in, numerical models.
Book: Thermal Spray Technology
Series: ASM Handbook
Volume: 5A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v05a.a0005727
EISBN: 978-1-62708-171-9
Abstract
This article discusses three types of powder-feeder systems that are commonly used throughout the thermal spray (TS) industry: gravity-based devices, rotating wheel devices, and fluidized-bed systems. It provides information on the various mechanical methods for producing powders, namely, crushing, milling, attriting, and machining. The article describes two prime methods of agglomeration. One method uses a binder by way of agglutination, while the other relies on a sintering operation. The article discusses the technology and principles of the processes that relate to thermal spraying, and offers an understanding for choosing particular feedstock materials that are classified based on the thermal spray process, material morphology, chemical nature of the material, and applications. Sieving, the most common method of separating powders into their size fractions, is also reviewed. The article also provides information on the topical areas and precautions to be undertaken to protect the operator from safety hazards.
Book Chapter
Series: ASM Handbook
Volume: 23A
Publisher: ASM International
Published: 12 September 2022
DOI: 10.31399/asm.hb.v23A.a0006885
EISBN: 978-1-62708-392-8
... the Clausius-Clapeyron relation: (Eq 19) P sat ( T su ) = 1 + β r 2 × P atm × exp ( M a L v R ( 1 T v − 1 T su ) ) Modeling of Free Melt Pool Surface In laser-based metal AM, the melt pool surface...
Abstract
This article focuses on the directed-energy deposition (DED) additive manufacturing (AM) technique of biomedical alloys. First, it provides an overview of the DED process. This is followed by a section describing the design and development of the multiphysics computational modeling of the layer-by-layer fusion-based DED process. A brief overview of the primary governing equations, boundary conditions, and numerical methods prescribed for modeling laser-based metal AM is then presented. Next, the article discusses fundamental concepts related to laser surface melting and laser-assisted bioceramic coatings/composites on implant surfaces, with particular examples related to biomedical magnesium and titanium alloys. It then provides a review of the processes involved in DED of biomedical stainless steels, Co-Cr-Mo alloys, and biomedical titanium alloys. Further, the article covers novel applications of DED for titanium-base biomedical implants. It concludes with a section on the forecast of DED in biomedical applications.
Series: ASM Handbook
Volume: 5A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v05a.9781627081719
EISBN: 978-1-62708-171-9