[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-665339-105":59,"doc-detail-665339-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","phase-equilibrium-and-the-phase-rule-lecture-contents","Phase Equilibrium And The Phase Rule - Lecture Contents","","This lecture explains phase equilibrium and the phase rule using core concepts of components, phases, and states of matter. It defines phase change and clarifies that phases can be characterized by independent variables. The lecture presents Willard Gibbs’ phase rule F = C − P + 2, interpreting C, P, and degrees of freedom for equilibrium. It also describes how phase diagrams visualize regions of solid, liquid, and gas, using equilibrium curves to indicate coexistence conditions and phase-change boundaries.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/phase-equilibrium-and-the-phase-rule-lecture-contents/665339/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/phase-equilibrium-and-the-phase-rule-lecture-contents/665339.png","ImageObject",300,407,{"name":92,"@type":93},"RuangKosong","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the phase rule and how does it determine degrees of freedom?","Question",{"text":112,"@type":113},"The lecture states that Willard Gibbs formulated the phase rule, expressed as F = C − P + 2. F is the number of degrees of freedom, meaning the least number of intensive variables that must be fixed to describe the system completely in equilibrium.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What are components, states of matter, and phases in this lecture?",{"text":117,"@type":113},"A component is a substance with a defined chemical structure. A state of matter is a form matter can take at given temperature and pressure (solid, liquid, gas), while a phase is a portion of the material with uniform chemical and physical properties separated by a boundary.",{"name":119,"@type":110,"acceptedAnswer":120},"How do phase diagrams show phase changes and coexistence?",{"text":121,"@type":113},"Phase diagrams visualize phase behavior as charts of one system variable against another, typically pressure versus temperature. The diagram is divided into regions for solid, liquid, and gas, and equilibrium curves indicate conditions where two phases coexist; crossing these lines corresponds to phase changes.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},665339,1793298833,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962090883219,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Phase Equilibrium And The Phase Rule  \nContents  \nIn this lecture you will learn:  \n Definition of phase and phase rule  \n Definition supercritical fluid and its use  \n Types of phase diagrams :  \na. Single component phase diagrams: water and CO2 phase diagrams as examples  \nb. Two component phase diagrams  \nc. Three component phase diagrams  \nDefinitions  \nComponent: is a substance in a system with a defined chemical structure.  \n State of matter: is a form that matter can take at certain temperature and pressure.Examples are solid, liquid, gas.  \n The states of matter can exist in different phases.  \n Phase :  \n[a. is](a. is) the form of matter that has uniform chemical and physical properties.  \nb. It is a homogenous, physically distinct and mechanically separable portion of the material with a given chemical composition and structure.  \nc. It is separated from other portions in the system by a boundary.  \nDefinitions  \n When a phase in one form is altered to another form, a“phase change” is said to have occurred.  \n When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties.  \n Each phase can be defined by a series of independent variablesThus: to understand and define the state of  \neach phase, knowledge of several variables is required  \nIce + water system is One component Two Phase system  \nPhase rule  \n Willard Gibbs formulated the phase rule, which is a relationship for determining the least number of variables (e.g., temperature, pressure, density, concentration, etc.) required to define the state of the system, or the number of variables which can be changed without changing the equilibrium state of the system.  \n This critical number is called F, the number of degrees of freedom of the system, and  \nthe rule is expressed as follows:  \nF= C – P+ 2  \nPhase rule  \nWhere : C is the number of components (the number of components is the smallest number of constituents by which the composition of each phase in the system at equilibrium can be expressed in the form of a chemical formula or equation)  \n P is the number of phases present  \n Thus: the number of degrees of freedom (F) is the least number of intensive variables that must be fixed/known to describe the system completely  \n As the number of components increases (i.e, system becomes more complex), so do the required degrees of freedom needed to define the system (necessary to fix more variables to define the system) .  \nPhase rule  \nPhase Diagrams = phase equilibrium diagrams  \n At most temperatures and pressures, a single pure substance at equilibrium exists entirely as a solid, liquid, or gas.  \n BUT at certain temperatures and pressures, two and even all three phases may coexist.  \n Example: Pure water at  \na. 130 C and 1 atm is gas  \nb. 40 C and 10 atm is solid  \nc. 100 C and 1 atm may be a gas, Liquid, or a mixture of both  \nd. 0.0098 C and 4.58 mm Hg may be a solid, a gas, a liquid, or a  \nmixture  \nPhase rule  \nPhase Diagrams = phase equilibrium diagrams  \n The phase diagram is a useful tool to visualize phase behavior.  \n It is a chart or a graph of one system variable against another.  \n (Relationship between composition of different phases and variables)  \n It give details on conditions at which the substance phases exist as solid, liquid or gas in equilibrium with each other.  \nPhase rule  \nPhase diagram for a generic single-component system  \nA typical phase diagram has pressure on the y-axis (typically in atmospheres) and temperature on the x-axis (typically in degrees Celsius or Kelvin) .  \nThe diagram is divided into three areas, which represent the solid, liquid, and gaseous states of the substance.  \nThe lines are known as “equilibrium curves”: any point on these curves represent two phases which exist in equilibrium at certain temperature and pressure.  \nPhase rule  \nPhase diagram for a generic single-component system  \n As we cross the lines or curves on the phase diagram, a p","cbCaiariRWRuoBOS","https://ap.wps.com/l/cbCaiariRWRuoBOS","pdf",1252956,32,"English","# Contents\n## Definition of phase and phase rule\n## Definition of supercritical fluid and its use\n## Types of phase diagrams","[{\"question\":\"What is the phase rule and how does it determine degrees of freedom?\",\"answer\":\"The lecture states that Willard Gibbs formulated the phase rule, expressed as F = C − P + 2. F is the number of degrees of freedom, meaning the least number of intensive variables that must be fixed to describe the system completely in equilibrium.\"},{\"question\":\"What are components, states of matter, and phases in this lecture?\",\"answer\":\"A component is a substance with a defined chemical structure. A state of matter is a form matter can take at given temperature and pressure (solid, liquid, gas), while a phase is a portion of the material with uniform chemical and physical properties separated by a boundary.\"},{\"question\":\"How do phase diagrams show phase changes and coexistence?\",\"answer\":\"Phase diagrams visualize phase behavior as charts of one system variable against another, typically pressure versus temperature. The diagram is divided into regions for solid, liquid, and gas, and equilibrium curves indicate conditions where two phases coexist; crossing these lines corresponds to phase changes.\"}]","Phase Equilibrium And The Phase Rule - Lecture Contents | PDF",81]