[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-266548-105":59,"doc-detail-266548-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","thermodynamics-equations-key-relations","Thermodynamics Equations - Key Relations","","Thermodynamics equations summary covering core relationships for pressure variation with depth in fluids, hydrostatic absolute and gage pressure, and mechanical energy terms including kinetic and potential energy. Includes specific heat relations for ideal gases, formulas for energy transfer by work with electrical and mechanical work modes, and work for constant force and boundary cases. Also covers internal energy, enthalpy, and specific heats, P–v/T–v state characterization for superheated, compressed, and saturated-vapor mixture regions, plus ideal Rankine cycle definitions and entropy principles with isentropic and efficiency relations for steady-flow devices.",{"@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":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/thermodynamics-equations-key-relations/266548/",{"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/thermodynamics-equations-key-relations/266548.png","ImageObject",300,407,{"name":92,"@type":93},"Sage","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-20","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you relate pressure variation with depth for points in the same fluid?","Question",{"text":112,"@type":113},"Apply the hydrostatic pressure relation between two points in the same fluid, using “below” and “above” to reference lower and higher elevations.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What equations are used to compute energy transfer by work, and how is the sign convention defined?",{"text":117,"@type":113},"Use the sign convention that work done on a system is (+) and work done by a system is (-), with separate expressions for electrical work and mechanical work forms such as shaft, spring, and boundary work.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you determine entropy change for isothermal, internally reversible, and isentropic processes?",{"text":121,"@type":113},"For isothermal heat transfer, use the given entropy transfer relation at constant temperature. For internally reversible processes, compare entropy at states, and for isentropic processes apply ΔS = 0 (or S2 = S1).","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},266548,1789408842,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},687197207057,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","􀜹􀝁􀝅􀝃ℎ􀝐, 􀜹 = 􀝉􀝃  \nWhere m=mass, g=gravitational acceleration  \n􀜦􀝁􀝊􀝏􀝅􀝐􀝕, 􀟩 =  \n􀝉  \n ~~ 􀜸~~   \nWhere m=mass, ~~V~~ =Volume  \n􀜵􀝌􀝁􀜿􀝅􀝂􀝅􀜿 􀝒􀝋􀝈􀝑􀝉􀝁 , 􀝒 = 􀜸􀝉 = 1􀟩􀜵􀝌􀝁􀜿􀝅􀝂􀝅􀜿 􀝃􀝎􀜽􀝒􀝅􀝐􀝕, 􀜵􀜩 = 􀟩   \n􀟩 􀯁2 􀯈  \nWhere rH2O =1000 kg/m3  \n􀜲􀯚􀯔􀯚􀯘 = 􀜲􀮺􀯕􀯦 − 􀜲􀯔􀯧􀯠 􀜲􀯩􀯔􀯖 = 􀜲􀯔􀯧􀯠 − 􀜲􀯔􀯕􀯦  \nVariation of pressure with depth: Apply between two points in the same fluid. Where “below” refers to point at lower elevation and “above” at higher elevation  \n􀜲􀯕􀯘􀯟􀯢􀯪 = 􀜲􀯔􀯕􀯢􀯩􀯘 + 􀟩􀝃 ∆􀝖  \nThe absolute and gage pressures in a liquid open to the atmosphere at a depth of h from the free surface are:  \n􀜲 = 􀜲􀯔􀯧􀯠 + 􀟩􀝃ℎ 􀜲􀯚􀯔􀯚􀯘 = 􀟩􀝃ℎ  \nKinetic Energy:  􀜸 2   􀜸 2   􀝇􀜬   \nWhere m=mass, 􀜭􀜧 = 􀝉 2 (􀝇􀜬) 􀝇􀝁 = 2 (􀝇􀝃 ) V=velocity  \nP~~otential ~~En~~ergy~~: 􀜲􀜧 = 􀝉􀝃􀝖 (􀝇􀜬) 􀝌􀝁 = 􀝃􀝖 (􀝇􀝇􀜬􀝃) Where m=mass, g=gravitational acceleration, z=elevation  \nSPECIFIC HEAT RELATIONS FOR IDEAL GAS:  \nVariation of spec. heats with T is [smooth and may be approx. as](smooth and may be approx. as) linear over small T interval. Can replace specific heat with Cavg, yielding:  \n􀝑2 − 􀝑1 = 􀜿􀯩,􀯔􀯩􀯚 􀜶2 − 􀜶1 , ℎ2 − ℎ1 = 􀜿 􀯣 ,􀯔􀯩􀯚 (􀜶2 − 􀜶1 )  \n 􀝇􀜬   􀜿􀯣   \n􀜿􀯣 = 􀜿􀯩 + 􀜴  􀝇 −  \n􀝇􀝃􀜭 , 􀜿􀯩  \nENERGY TRANSFER BY WORK:  \nSign convention: Work done on a system = (+)  \nWork done by a system = (-)  \n\n| Electrical Work:\u003Cbr>WmhoevnetNhrCoouughlomba postofentelecial dtrificfeal charencergVe 􀜹􀯘 = 􀜸􀜰 Electrical work done during a time interval 􀀧t:\u003Cbr>2 |  |  |  |  | In the rate form, 􀜹􀯘 = 􀜸􀜫 = 􀜫 2􀜴 = 􀜸􀜴2~~ ~~ (􀜹) Where 􀜹􀯘 is the electrical power and I is the current. |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 􀜹􀯘 = 􀜸􀜫 􀝀􀝐 (􀝇􀜬) Or when V and I remain constant during interval 􀀧t:\u003Cbr>1 􀜹􀯘 = 􀜸􀜫 ∆􀝐 (􀝇􀜬) |  |  |  |  |  |  |  |  |  |\n| Mechanical Forms of Work:\u003Cbr>􀜹 = 􀜨􀝏 (􀝇􀜬) |  |  | Shaft Work: 􀜹􀯦ℎ = 2􀟨 􀝊 􀜶 (􀝇􀜹) Where 􀝊 is the number of revolutions per unit time\u003Cbr>Spring Work: 􀜹􀯦􀯣􀯥􀯜􀯡􀯚 = 12 􀝇 􀝔22 􀝔12 (􀝇􀜬)\u003Cbr>Where x1 and x2 are the initial and final displacements ofthe spring. |  |  |  |  |  |  |\n| 2\u003Cbr>􀜹 = 􀜨􀝀􀝏 1 | (􀝇􀜬) |  |  |  |  |  |  |  |  |\n| Work done by a constant force, Fon a body displaced a distance s |  |  |  |  |  |  |  |  |  |\n| Boundary Work: |  | 􀜲 (~~􀜸2~~ − ~~􀜸1~~)\u003Cbr>􀜲2 ~~ 􀜸2~~ − 􀜲1 ~~ 􀜸1~~\u003Cbr>1 − 􀝊 |  | 􀝉􀜴 (􀜶2 −􀜶1)\u003Cbr>Polytropic Ideal Gas 􀜹􀯕 = ~~ ~~\u003Cbr>process: 1 − 􀝊 |  |  |  |  |  |\n| 2 􀜹􀯕 = 􀜲􀝀􀝒\u003Cbr>1 | (􀝇􀜬) |  |  |  |  |  |  |  |  |\n| Constant P process: 􀜹􀯕 =\u003Cbr>Polytropic process: 􀜹􀯕 = |  |  |  | Polytropic Isothermal Ideal Gas process: |  | 􀜹􀯕 = 􀜲􀜸 􀝈􀝊 | \u003Cbr>􀜸2 􀜸1 | = 􀝉􀜴􀜶􀯢 􀝈􀝊 | \u003Cbr>􀜸2 􀜸1 |\n|  |  |  |  | During actual exp/comp process of gases, P and ~~V~~ are related by P~~V~~n=C. Where n and C are constants therefore between 2 states, ideal gas, closed\u003Cbr>􀜥 = 􀜲1 ~~ 􀜸1~~ = 􀜲2 ~~ 􀜸2~~ = mR􀜶0 ∴ 􀯏􀯏~~2~~1 = 􀯉􀯉~~2~~1\u003Cbr>|  |  |  |  |  |\n\nINTERNAL ENERGY, ENTHALPY & SPECIFIC HEATS OF SOLIDS & LIQUIDS  \nFor an incompressible substance: 􀜿􀯣 = 􀜿􀯩 = 􀜿  \n 􀝇􀜬   \n∆􀝑 = 􀝑2 − 􀝑1 = 􀜿􀯔􀯩􀯚 􀜶2 − 􀜶1 ( )  \n􀝇􀝃  \n∆ℎ = ∆􀝑 + 􀝒∆􀜲 ≅ 􀜿􀯔􀯩􀯚 􀜶2 − 􀜶1 + 􀝒∆􀜲 (􀝇􀝇􀜬􀝃)  \nLIQUID  \nv, h, u,  \nLIQUID  \nLiq vap  \nP-v Diagram T-v Diagram  \nSUPERHEATED STATE  \nRegion to the right of sat vap line & at a T above Tcr To determine if S.H.  \nP\u003CPsat at given T 􀜳􀝑􀜽􀝈􀝅􀝐􀝕, 􀝔 = 1  \nT> Tsat at given P  \nv>vg at given P or T  \nu> ug at given P or T  \nh> hg at given P or T  \ns> sg at given P or T  \nCOMPRESSED STATE  \nRegion to the left of the Sat Liq line  \n[In the absence of C.L. data](In the absence of C.L. data) – treat a C.L. as a Sat liq at given T  \n􀝕􀯙 ≅ 􀝕􀯙@􀯍 Where y is v, u, s or h  \nTo determine if C.L.  \nP>Psat at given TT\u003C Tsat at given Pv\u003C vf at given P or Tu\u003C uf at given P or Th\u003C hf at given P or Ts\u003C sf at given P or T  \n􀜳􀝑􀜽􀝈􀝅􀝐􀝕, 􀝔 = 0  \nSATURATED -VAPOR MIXTURE STATE  \nRegion under the dome  \nTo determine the proportion of liquid and vapor phases in the mixture, find quality, x  \n􀝉􀯩􀯔􀯣􀯢􀯥  \n􀝔 =  \n􀝉 􀯧􀯢􀯧􀯔􀯟  \n, 􀝉 􀯧􀯢􀯧􀯔􀯟 = 􀯠 􀳗􀳔􀳜+􀯠 􀳡􀳌􀳛 =􀯠 􀳑+􀯠􀳒  \n􀜳􀝑􀜽􀝈􀝅􀝐􀝕, 0 \u003C 􀝔 \u003C 1  \nTo find s at state 1.  \nWhere y is v, u, s or h  \n􀝕1 = 􀝕􀯙 + 􀝔 􀝕􀯚 − 􀝕􀯙  \nTo determine if Sat - Mixture.  \n􀝒􀯙 ≤ 􀝒 ≤ 􀝒􀯚  \n􀝑􀯙 ≤ 􀝑 ≤ 􀝑􀯚ℎ􀯙 ≤ ℎ ≤ ℎ􀯚  \n􀝏􀯙 ≤ 􀝏 ≤ 􀝏􀯚  \nIDEAL RANKINE CYCLE:  The ideal c","cbCaiqTy2YWRogWU","https://ap.wps.com/l/cbCaiqTy2YWRogWU","pdf",876907,"English","# Pressure and Energy Relations\n## Hydrostatics and Energy Forms\n## Specific Heat Relations for Ideal Gas\n## Energy Transfer by Work\n# State Properties and Phase Regions\n## Internal Energy, Enthalpy, Specific Heats\n## Superheated, Compressed, and Saturated Mixtures\n# Rankine Cycle and Entropy\n## Ideal Rankine Cycles\n## Entropy Change and Isentropic Processes\n## Steady-Flow Device Efficiencies","[{\"question\":\"How do you relate pressure variation with depth for points in the same fluid?\",\"answer\":\"Apply the hydrostatic pressure relation between two points in the same fluid, using “below” and “above” to reference lower and higher elevations.\"},{\"question\":\"What equations are used to compute energy transfer by work, and how is the sign convention defined?\",\"answer\":\"Use the sign convention that work done on a system is (+) and work done by a system is (-), with separate expressions for electrical work and mechanical work forms such as shaft, spring, and boundary work.\"},{\"question\":\"How do you determine entropy change for isothermal, internally reversible, and isentropic processes?\",\"answer\":\"For isothermal heat transfer, use the given entropy transfer relation at constant temperature. For internally reversible processes, compare entropy at states, and for isentropic processes apply ΔS = 0 (or S2 = S1).\"}]","Thermodynamics Equations - Key Relations | PDF",13]